Question

In: Finance

a. The cost of a new automobile is $11,200. If the interest rate is 8%, how...

a. The cost of a new automobile is $11,200. If the interest rate is 8%, how much would you have to set aside now to provide this sum in eight years? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Present value            $

b. You have to pay $15,000 a year in school fees at the end of each of the next nine years. If the interest rate is 11%, how much do you need to set aside today to cover these bills? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Present value            $

c. You have invested $135,000 at 11%. After paying the above school fees, how much would remain at the end of the nine years? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Future value            $

Solutions

Expert Solution

Answer a.

Cost of Automobile = $11,200
Interest Rate = 8%
Period = 8 years

Amount Deposited = Amount required / (1 + i)^n
Amount Deposited = $11,200 / 1.08^8
Amount Deposited = $6,051.01

So, you need to set aside $6,051.01 today to have $11,200 after 8 years

Answer b.

Annual Payment = $15,000
Interest Rate = 11%
Number of years = 9

Present Value = $15,000/1.11 + $15,000/1.11^2 + $15,000/1.11^3 + … + $15,000/1.11^9
Present Value = $15,000 * (1 - (1/1.11)^9) / 0.11
Present Value = $15,000 * 5.5370
Present Value = $83,055

So, you need to set aside $83,055.00 today to cover these annual expenses

Answer c.

Future Value of Amount Invested = $135,000 * 1.11^9
Future Value of Amount Invested = $345,334.98

Future Value of Annual Payment = $15,000*1.11^8 + $15,000*1.11^7 + … + $15,000*1.11 + $15,000
Future Value of Annual Payment = $15,000 * (1.11^9 - 1) / 0.11
Future Value of Annual Payment = $15,000 * 14.16397
Future Value of Annual Payment = $212,459.55

Balance after 9 years = $345,334.98 - $212,459.55
Balance after 9 years = $132,875.43


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