FIN. HW 2
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?
$1,540.29 1650 = Present value*(1+0.035)^2
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 (2.2*1000000)/1.036^4.5 =$1,876,306.49
Precision Engineering invested $95,000 at 5.5 percent interest, compounded annually for 2 years. How much interest did the company earn over this period of time?
$10,737.38
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 5500*(1+0.065)^5= 7535.48 7535.48 +2500= 10035.48 10035.48*(1+0.05)^5= $12,808.09
You are due to receive a lump-sum payment of $1,350 in four years and an additional lump-sum payment of $1,450 in five years. Assuming a discount rate of 2.0 percent interest, what would be the value of the payments today?
$2,560.50 Present value=Cash flow*Present value of discounting factor(rate%,time period) =1350/1.02^4+1450/1.02^5 =$2,560.50
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?
$31,476.80 $35,000 / (1+0.036)^3 = $35,000 / 1.11193 = $31,476.80
Your parents spent $7,800 to buy 200 shares of stock in a new company 12 years ago. The stock has appreciated 14.6 percent per year on average. What is the current value of those 200 shares?
$40,023.03 7800(1+0.146)^12= $40,023.03
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?
$6,018.3 present value = 6500/(1.026)^3=$6,018.3
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?
$7,295.71 5000(1+0.065)^6= $7,295.71
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.
1.56 years t = ln(FV / PV) / ln(1 + r) t = ln($42,650 / $40,000) / ln 1.042 t = 1.56 years
How long will it take to double your savings if you earn 6.4 percent interest, compounded annually?
11.17 years $2 = $1 ×(1 + .064)t
At 10 percent interest, how long does it take to triple your money?
11.53 years
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?
1540.57 = $ 1350 ( 1+ 0.045)^3 = $ 1350 (1.045^3) = $ 1350 * 1.1412 = $ 1540.57
You just won $17,500 and deposited your winnings into an account that pays 6.7 percent interest, compounded annually. How long will you have to wait until your winnings are worth $50,000?
16.19 50,000=17500*(1.067)^n (50,000/17500)=(1.067)^n og (50,000/17500)=n*log 1.067 n=log (50,000/17500)/log 1.067 =16.19 years
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?
2182.208616 2350=x(1+0.025)^3 = 2182.208616 (mathway)
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?
24.57% future Value = $900 (Triple of $300) Present Value = $300 Time = 5 Years $900 = $300 * (1+Interest rate)^5 $900 / $300 = (1+Interest rate)^5 $3 = (1+Interest rate)^5 5√$3 = (1+Interest rate) Calculating 5th time root of $3 we get = 1.2457 1.2457 = (1+Interest rate) 1.2457 - 1 = Interest rate 0.2457 or 24.57% Interest Rate = 24.57%
What is the future value of $8,000 invested today and held for 15 years at 8.5 percent compounded annually?
27,197.94 8,000*(1+0.085)^15 = 8,000*3.3997 =27,197.94
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?
29818.16 Present value = 60000/(1+6%)^12 = 29818.16
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?
3205.642293 $10 x (1 + 0.051) ^ 116 = 3205.642293
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 $50,000 = $5,000× (1 + .065)t t = 36.57 years Wait time = 1 + 36.57 = 37.57 years
You deposit $1,675 into an account that earns 2.35 percent interest in two years. If you deposit an additional $1,950 in the same account 2 years later, how much would be in the account six years from now?
3880.81 Future value of 1675 after 2 years at 2.35% = 1675 * (1+0.0235)^2 = 1754.65001875 Total value after adding 1950 = 1950 + 1754.65001875 = 3704.65001875 Value of 3704.65001875 after 2 years from 5 years later = 3704.65001875 * (1+0.0235)^2 = 3880.81
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?
3900 $3000+(3000*.03*10) =3000+900=3900
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.
4.09 $50,000 = $15,000 * (1 + r)^30 3.3333 = (1 + r)^30 1.0409 = 1 + r r = 0.0409
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 ($2,500*5*3.6)/100 = 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 11500(1+0.0055)^6= 11884.75655 11884.75655-11500= 384.75655 11500(0.0055)(6)= 379.5 384.75655-379.5= 5.25655
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?
5000(1+0.05)^35= $27,580.08 5000(1+0.05)^35= 21,609.71
Jenny needs to borrow $5,500 for four years. The loan will be repaid in one lump sum at the end of the loan term. Which one of the following interest rates is best for Jenny?
6.5 percent simple interest
You have $2,000 today in your savings account. How long must you wait for your savings to be worth $4,500 if you are earning 1.25 percent interest, compounded annually?
65.28 4500=2000(1+0.0125)^x log(4500/2000)/log(1+0.0125)= 65.28
Lisa has $1,000 in cash today. Which one of the following investment options is most apt to double her money?
8 percent interest for 9 years 1000(1+0.08)^9= 2000 (double)
You want to invest an amount of money today and receive back twice that amount in the future. You expect to earn 9 percent interest. Approximately how long must you wait for your investment to double in value?
8 years
Which one of the following will increase the present value of a lump-sum future amount to be received in 15 years?
A decrease in the interest rate
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 = $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
The future value of a lump-sum investment will increase if you:
Increase the time period
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
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.
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.
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.
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. Ans earn $8 more than if he had invested with his credit union Future value of credit union = 3600 + (3600 * 22% *5 years) = $ 3996 Future value of Compass = $ 3600 + ( 1 + 2.15%) = $ 4004 Difference = $ 4004 - $ 3996 = $ 8
Marcos is investing $5 today at 7 percent interest so he can have $35 later. This $35 is referred to as the:
future value
The present value of a lump-sum future amount:
increases as the interest rate decreases.
All else held constant, the future value of a lump-sum investment will decrease if the:
interest is changed to simple interest from compound interest.
Jamie earned $14 in interest on her savings account last year. She has decided to leave the $14 in her account so that she can earn interest on the $14 this year. The interest earned on last year's interest earnings is called:
interest on interest.
The relationship between the present value and the investment time period is best described as:
inverse
Given an interest rate of zero percent, the future value of a lump sum invested today will always:
remain constant, regardless of the investment time period.
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:
will be greater if you invest with Northern Bank. 500 / (1 + 2.5%)^2 = 1427.72 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
