BCOR 340 HW 2
Jessica invested $2,000 today in an investment that pays 6.5 percent annual interest. Which one of the following statements is correct, assuming all interest is reinvested?
she could have the same future value and invest less than $2,00 initially if she could earn more than 6.5 percent interest
You're trying to save to buy a new car valued at $42,650. You have $40,000 today that can be invested at your bank. The bank pays 4.2 percent annual interest on its accounts. How long will it be before you have enough to buy the car for cash? Assume the price of the car remains constant.
t = ln(FV / PV) / ln(1 + r) t = ln($42,650 / $40,000) / ln 1.042 t = 1.56 years
The relationship between the present value and the investment time period is best described as:
inverse.
By definition, a bank that pays simple interest on a savings account will pay interest:
only on the principal amount originally invested
Rob wants to invest $15,000 for 7 years. Which one of the following rates will provide him with the largest future value?
4 percent interest, compounded annually
You are due to receive a lump-sum payment of $1,350 in five years. If you could invest that money at 4.5 percent interest for three years, how much would it be worth eight years from now?
$1,540.57
Starlite Industries will need $2.2 million 4.5 years from now to replace some equipment. Currently, the firm has some extra cash and would like to establish a savings account for this purpose. The account pays 3.6 percent interest, compounded annually. How much money must the company deposit today to fully fund the equipment purchase?
$1,876,306.49
Ten years ago, you deposited $5,500 into an account. Five years ago, you added an additional $2,500 to this account. You earned 6.5 percent, compounded annually, for the first 5 years and 5.0 percent, compounded annually, for the last 5 years. How much money do you have in your account today?
$12,808.09
You have just made your first $5,000 contribution to your retirement account. Assuming you earn a rate of return of 5 percent and make no additional contributions, what will your account be worth when you retire in 35 years? What if you wait for 5 years before contributing?
$27,580.08; $21,609.71
Twelve years from now, you will be inheriting $60,000 What is this inheritance worth to you today if you can earn 6.0 percent interest, compounded annually?
$29,818.16
You are due to receive a lump-sum payment of $1,750 in three years and an additional lump-sum payment of $1,850 in five years. Assuming a discount rate of 3.0 percent interest, what would be the value of the payments today?
$3,197.32
You want to have $32,000 for a down payment on a house 5 years from now. If you can earn 4.3 percent, compounded annually on your savings, how much do you need to deposit today to reach your goal?
$32000 = PV * (1 + 4.3%)5 $32000 = PV * (1 + 0.043)5 $32000 = PV * (1.043)5 $32000 = PV * 1.23430231101 PV = $32000 / 1.23430231101 PV = $25925.58
Western Bank pays 5 percent simple interest on its savings account balances, whereas Eastern Bank pays 5 percent compounded annually. If you deposited $6,000 in each bank, how much more money would you earn from the Eastern Bank account at the end of 3 years?
$45.75
Today, you deposit $2,500 in a bank account that pays 3.6 percent simple interest. How much interest will you earn over the next 5 years?
$450.00
Roberto just deposited $11,500 into his savings account at Security Savings Bank. The bank will pay .55 percent interest, compounded annually, on this account. How much interest on interest will he earn over the next 6 years?
$5.26
Isaac only has $1,090 today but needs $1,979 to buy a new computer. How long will he have to wait to buy the computer if he earns 5.4 percent compounded annually on his savings? Assume the price of the computer remains constant.
11.34 years
Assume the total cost of a college education will be $325,000 when your child enters college in 16 years. You presently have $40,000 to invest and do not plan to invest anything further. What annual rate of interest must you earn on your investment to cover the entire cost of your child's college education?
325,000=40000(FVIFi,16) FVIFi,16= 325,000/40000 FVIFi,16=8.125 when we look in the table of FVIF in the year 16 we find 8.137 the very nearby amount to our 8.125 in the 14% rate interest column. so because 8.137 is little bit higher than our answerd amount 8.125 so the rate interest is little bit lower than the 14% i.e 13.99 is the right answer that is given in our problem. so the applicable rate of interest that will be charged on $ 40000 to get $ 325,000 is 13.99%
You expect to receive $5,000 at graduation one year from now. Your plan is to invest this money at 6.5 percent, compounded annually, until you have $50,000. At that time, you plan to travel around the world. How long from now will it be until you can begin your travels?
37.57 years
You are scheduled to receive $5,000 in two years. When you receive it, you will invest it at 6.5 percent per year. How much will your investment be worth eight years from now?
5000*(1+0.065)^6 $ 7,295.71
Suppose that in 2015, a $10 silver certificate from 1898 sold for $11,700. For this to have been true, what would the annual increase in the value of the certificate have been?
6.22 percent
You deposit $1,200 into an account that earns 1.75 percent interest in three years. If you deposit an additional $1,200 in the same account 2 years later, how much would be in the account six years from now?
Amount Deposited in Year 3 = $1,200 Amount Deposited in Year 5 = $1,200 Annual Interest Rate = 1.75% Future Value 6 Years from Now = $1,200*1.0175^3 + $1,200*1.0175 Future Value 6 Years from Now = $1,264.11 + $1,221.00 Future Value 6 Years from Now = $2,485.11
Stephen claims that he invested $6,000 six years ago and that this investment is worth $28,700 today. For this to be true, what annual rate of return did he have to earn? Assume the interest compounded annually.
Annual Percentage rate =>[ ($28,700/$6,000)1/6 - 1] × 100% = 29.80 percent
Your coin collection contains ten 1949 silver dollars. If your grandparents purchased the coins for their face value when they were new, how much will your collection be worth when you retire in 2065, assuming the coins appreciate at an annual rate of 5.1 percent?
Collection of 10 1949 silver dollars was worth $10 in 1949. If annual rate is 5.1% its value 116 years later in 2065 using the formula P(1 + i) ^ n would be $10 x (1 + 0.051) ^ 116 = $3,205.64 Thus value of the collection in 2065 would be $3,205.64
Today, Georgia is investing $24,000 at 5.5 percent, compounded annually, for 6 years. How much additional income could she earn if she had invested this amount at 6.5 percent, compounded annually?
FV = $24000 * (1 + 5.5%)6 FV = $24000 * (1 + 0.055)6 FV = $24000 * (1.055)6 FV = $24000 * 1.37884280676 FV = $33092.2273 Now, we will calculate the income earned: Income = Future value - Present value Income = $33092.2273 - $24000 Income = $9092.2273 Calculation of income at 6.5%: Now we will calculate the future value of investing $24000 at 6.5% by using the following formula: FV = PV * (1 + r%)n where, FV = Future value, PV = Present value = $24000, r = rate of interest = 6.5%, n= time period = 6 now, putting theses values in the above equation, we get, FV = $24000 * (1 + 6.5%)6 FV = $24000 * (1 + 0.065)6 FV = $24000 * (1.065)6 FV = $24000 * 1.45914229654 FV = $35019.41511 Now, we will calculate the income earned: Income = Future value - Present value Income = $35019.41511 - $24000 Income = $11019.41511 Additional income by investing $24000 at 6.5% is: Additional income = Income at 6.5% - Income at 5.5% Additional income = $11019.42 - $9092.23 Additional income = $1927.19
You have been told that you need $15,000 today for every $50,000 you want when you retire 30 years from now. What rate of interest was used in the present value computation? Assume interest is compounded annually.
FV = PV * (1 + r)n $50,000 = $15,000 * (1 + r)30 3.3333 = (1 + r)30 1.0409 = 1 + r r = 0.0409
Roberto just deposited $11,500 into his savings account at Security Savings Bank. The bank will pay .55 percent interest, compounded annually, on this account. How much interest on interest will he earn over the next 6 years?
FV = PV * (1 + r)n FV = $11,500 * (1 + 0.55%)6 FV = $11,500 * 1.033457 FV = $11,884.76 Total interest earned = $11,884.76 - $11,500 = $384.76 Now, we need to compute how much would the interest on interest be. Interest on Interest = Total Interest (computed above) - Simple Interest Simple Interest = Principal * rate * Time = $11,500 * 0.55% * 6 = $379.50 Interest on Interest = $384.76 - $379.50 = $5.26
What is the future value of $8,000 invested today and held for 15 years at 8.5 percent compounded annually?
FV= 8,000*(1+0.085)^15 = 8,000*3.3997 = 27,197.94.
You have $300 today and want to triple your money in 5 years. What interest rate must you earn if the interest is compounded annually?
Financial Calculator: N= 5 I%= Alpha solve PV= -300 PMT= 0 FV= 900 I%= 24.57
Theodoro has just received an insurance settlement of $18,500. She wants to save this money until her daughter goes to college. If she can earn an average of 5.2 percent, compounded annually, how much will she have saved when her daughter enters college 9 years from now?
Future value = Present value x (1 + interest rate)time period = $ 18,500 x 1.0529 = $ 18,500 x 1.57812594 = $ 29,195.33
You are due to receive a lump-sum payment of $1,650 in five years. Assuming a discount rate of 3.5 percent interest, what would be the value of the payment in Year 3?
Future value = present value*(1+ rate)^time 1650 = Present value(1+0.035)^2 Present value = 1540.29
Travis invests $5,500 today into a retirement account. He expects to earn 9.2 percent, compounded annually, on his money for the next 13 years. After that, he wants to be more conservative, so only expects to earn 6 percent, compounded annually. How much money will he have in his account when he retires 25 years from now, assuming this is the only deposit he makes into the account?
Hence A after 25 years=17268.59(1+6/100)^12 =$34,747.80 (approx)
Which one of the following is the correct formula for the current value of $600 invested today at 5 percent interest for 6 years?
PV = $600 / (1 + .05)6
Which one of the following is the correct formula for computing the present value of $600 to be received in 6 years? The discount rate is 7 percent.
PV = $600/(1 + .07)6
South Central Bank pays 2.5 percent interest, compounded annually, on its savings accounts. Northern Bank pays 2.5 percent simple interest on its savings accounts. You want to deposit sufficient funds today so that you will have $1,500 in your account 2 years from today. The amount you must deposit today:
Present Value at compounded annually = Investment / (1 + r)^n = 1500 / (1 + 2.5%)^2 = 1427.72 Future Value at Simple Interest = Principal + Principal* Rate * Time 1500 = x + x * 2.5% * 2 1.05x = 1500 x = 1428.57 Principal Invested with Northern Bank is $ 1428.57, Principal Invested with South Central Bank is $ 1427.72 Answer: will be greater if you invest with Northern Bank.
Katlyn needs to invest $5,318 today in order for her savings account to be worth $8,000 six years from now. Which one of the following terms refers to the $5,318?
Present value
You want to have $35,000 in cash to buy a car 3 years from today. You expect to earn 3.6 percent, compounded annually, on your savings. How much do you need to deposit today if this is the only money you save for this purpose?
Present value = $35,000/(1 + .036)3= $31,476.67
Your grandparents just gave you a gift of $3,000. You are investing this money at 3 percent simple interest. How much money will you have at the end of the 10 years?
So the Future value =$3000+(3000*.03*10) =3000+900=3900
You and your sister are planning a large anniversary party 3 years from today for your parents' 50th wedding anniversary. You have estimated that you will need $6,500 for this party. You can earn 2.6 percent compounded annually on your savings. How much would you and your sister have to deposit today in one lump sum to pay for the entire party?
So we need to calculate the present value of $6,500 which earns 2.6% compounded annually. Present value=6500/(1.026)3=$6,018.3
Sixty years ago, your grandparents opened two savings accounts and deposited $250 in each account. The first account was with City Bank at 3.6 percent, compounded annually. The second account was with Country Bank at 3.65 percent, compounded annually. Which one of the following statements is true concerning these accounts? (Do not round intermediate calculations.)
The Country Bank account has paid $61.30 more in interest than the City Bank account.
Which one of the following is a correct statement, all else held constant?
The future value is directly related to the interest rate.
The future value of a lump-sum investment will increase if you:
The future value of a lump-sum investment will increase if you:
Today, Charity wants to invest less than $3,000 with the goal of receiving $3,000 back some time in the future. Which one of the following statements is correct?
The period of time she has to wait decreases as the amount she invests increases.
Tomas earned $89 in interest on his savings account last year and has decided to leave the $89 in his account this coming year so it will earn interest. This process of earning interest on prior interest earnings is called:
compounding.
The interest rate used to compute the present value of a future cash flow is called the:
discount rate.
Computing the present value of a future cash flow to determine what that cash flow is worth today is called
discounted cash flow valuation
Calculating the present value of a future cash flow to determine its worth today is commonly called:
discounting cash flow valuation.
Lucas expects to receive a sales bonus of $7,500 one year from now. The process of determining how much that bonus is worth today is called:
discounting.
Lew has $3,600 that he wants to invest for 5 years. He can invest this amount at his credit union and earn 2.2 percent simple interest. Or, he can open an account at Compass Bank and earn 2.15 percent interest, compounded annually. If he decides to invest at Compass Bank for 5 years, he will:
earn $8 more than if he had invested with his credit union.
You are due to receive a lump-sum payment of $2,350 in seven years. Assuming a discount rate of 2.5 percent interest, what would be the value of the payment in Year 4?
explanation: 3 2.5 0 2,350.00N I/Y PV PMT FV- 2,182.21
Kendall is investing $3,333 today at 3 percent annual interest for three years. Which one of the following will increase the future value of that amount?
increasing the interest rate
