Ch 4 Quiz

The future value of a lump-sum investment will increase if you:

increase the time period.

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.

You have $6,800 to deposit. Regency Bank offers 6 percent per year compounded monthly (.5 percent per month), while King Bank offers 6 percent but will only compound annually. How much will your investment be worth in 20 years at each bank? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Regency Bank, Future Value = $ 22,509.39 King Bank ,Future Value =$ 21,808.52 Future Value = Present Value*(1+Rate)^Time Regency Bank, Future Value = $ 6800*(1+6%/12)^(20*12) = $ 22,509.39 King Bank , Future Value = $ 6800*(1+6%)^(20) = $ 21,808.52 Regency Bank, Future Value = $ 22,509.39 King Bank ,Future Value =$ 21,808.52

You have just made your first $4,500 contribution to your individual retirement account. Assume you earn an annual return of 11.0 percent and make no additional contributions. What will your account be worth when you retire in 45 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)b. What if you wait 10 years before contributing? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

$492,886.09 $173,586.83 a). FV of retirement account = Contribution * (1 + r)n = $4,500 * (1 + 0.11)45 = $4,500 * 109.5302 = $492,886.09 b). FV of retirement account = Contribution * (1 + r)n = $4,500 * (1 + 0.11)(45 - 10) = $4,500 * 38.5749 = $173,586.83

Which one of the following is the correct formula for the current value of $600 invested today at 5 percent interest for 6 years?

$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.

$600/(1 + .07)6

Although appealing to more refined tastes, art as a collectible has not always performed so profitably. Assume that in 2015, an auction house sold a statute at auction for a price of $10,426,500. Unfortunately for the previous owner, he had purchased it in 2010 at a price of $12,662,500. What was his annual rate of return on this sculpture? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

-3.81% A=P(1+r/100)^nwhereA=future valueP=present valuer=rate of interestn=time period. 10426500=12662500(1+r/100)^5 (10426500/12662500)^(1/5)=(1+r/100) (1+r/100)=0.961886474 r=(0.961886474-1)*100 =(3.81%)(Approx)(Negative).

Solve for the unknown number of years in each of the following: (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Present Value $400, $2091, $33105, $32800 Interest Rate 12%, 10%, 15%, 22% Future Value $1255, $3850, $388620, $202748

10.09 Years 6.40 Years 17.62 Years 9.16 Years Present value = 400 and Future value = 1255 at a rate of 12% We have Future value = Present value * ( 1 + r )n = 400 * (1.12)n = 1255 (1.12)n = 1255 / 400 = 3.1375 Take log on both sides n * Log (1.12) = Log (3.1375) n * 0.049218 = 0.496584 n = 0.496584 / 0.049218 = 10.09 Years Case - II Present value = 2091, Future value = 3850 at 10% 2091 * (1.10 )n = 3850 (1.10 )n = 3850 / 2091 = 1.841224 n * Log (1.10) = Log (1.841224) n * 0.041392685 = 0.26510663 n = 0.26510663 / 0.041392685 = 6.40 Years Case - III 33105 ( 1.15)n = 388620 ( 1.15)n = 388620 / 33105 = 11.73901223 n * Log (1.15) = Log ( 11.73901223) n * 0.06069784 = 1.06963156 n = 1.06963156 / 0.06069784 = 17.62 years Case - 4 32800 * ( 1.22)n = 202748 ( 1.22)n = 202748 / 32800 = 6.18134146 n * Log (1.22) = Log (6.18134146) n * 0.08635983= 0.791083 n = 0.791083 / 0.08635983 n = 9.16 Years

Assume the total cost of a college education will be $380,000 when your child enters college in 16 years. You presently have $62,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child's college education? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

12.00%

At 7.75 percent interest, how long does it take to quadruple your money? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

18.58 years. The rule of 144: To estimate how many years it will take to quadruple the money, we can use the rule of 144. 144/7.75 = 18.58 years.

You're trying to save to buy a new $245,000 Ferrari. You have $42,000 today that can be invested at your bank. The bank pays 4.9 percent annual interest on its accounts. How long will it be before you have enough to buy the car? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

37 Future value = 245000 and P = 42000 I = 4.9% FV = P * (1 + R)^N 245000 = 42000 * (1 + 4.9%)^N 1.049^N = 5.83333 Solving for N, we get N = 37 years

You need $79,000 in 8 years. If you can earn .46 percent per month, how much will you have to deposit today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

50848.99857 Amount invested today50848.99857(=79000/1.0046^96)Annual interest rate (monthly)0.46%Number of years5Number of months96Future Value$79,000.00

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

Assume that in 2018, a copper penny struck at the Philadelphia mint in 1796 was sold for $480,000. What was the rate of return on this investment?

8.29% Value in 1796= PV= 0.01 USD Value in 2018 = FV= 480000 USD Number of years= n= 2018-1796 = 222 FV= PV*(1+rate)^n 480000= 0.01*(1+r)^222 1+r= (480000/0.01)^(1/222) 1+r= 1.082929503 r= 1.082929503-1 = 0.082929503 Rate = 8.29%

At 7.75 percent interest, how long does it take to double your money? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

9.29 years. The rule of 72: in the rule of 72, we just have to divide 72 with the annual interest rate which will give you the estimated year for doubling the money 72/7.75 = 9.29 years.

Which one of the following will increase the present value of a lump-sum future amount to be received in 15 years? An increase in the interest rate A decrease in the future value Changing to compound interest from simple interest A decrease in the interest rate An increase in the time period

A decrease in the interest rate

Stacey deposits $5,000 into an account that pays 2 percent interest, compounded annually. At the same time, Kurt deposits $5,000 into an account paying 3.5 percent interest, compounded annually. At the end of three years:

Kurt will have a larger account value than Stacey will.

Which one of the following is a correct statement, all else held constant? The present value is directly related to the interest rate. The present value is inversely related to the future value. The period of time is directly related to the interest rate. The future value is inversely related to the period of time. The future value is directly related to the interest rate.

The future value is directly related to the interest rate.

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.

Lester had $6,270 in his savings account at the beginning of this year. This amount includes both the $6,000 he originally invested at the beginning of last year plus the $270 he earned in interest last year. This year, Lester earned a total of $282.15 in interest even though the interest rate on the account remained constant. This $282.15 is best described as:

compound interest

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.