Question

1.) You are graduating from college at the end of this semester and after reading The Business of Life box in this​ chapter, you have decided to invest ​$5,500 at the end of each year into a Roth IRA for the next 42 years. If you earn 7 percent compounded annually on your​ investment, how much will you have when you retire in 42 ​years? How much will you have if you wait 10 years before beginning to save and only make 32 payments into your retirement​ account?

2.) Mr. Bill S.​ Preston, Esq., purchased a new house for ​$60,000. He paid ​$25,000 upfront and agreed to pay the rest over the next 20 years in 20 equal annual payments that include principal payments plus 12 percent compound interest on the unpaid balance. What will these equal payments​ be?

3.)To pay for your​ child's education, you wish to have accumulated ​$14,000 at the end of 8 years. To do​ this, you plan to deposit an equal amount into the bank at the end of each year. If the bank is willing to pay 14 percent compounded​ annually, how much must you deposit each year to obtain your​ goal?

4.) How long will it take to pay off a loan of ​$52,000 at an annual rate of 12 percent compounded monthly if you make monthly payments of

​$650? Use five decimal places for the monthly percentage rate in your calculations.

Answer 1

1.a.Information provided:

Annual withdrawal= $5,500

Time= 42 years

Interest rate= 7%

The question is solved by calculating the future value of ordinary annuity.

Enter the below in a financial calculator to compute the future value of ordinary annuity:

PMT= -5,500

N= 42

I/Y= 7

Press the CPT key and FV to compute the future value of ordinary annuity.

The value obtained is 1,268,477.32.

Therefore, the amount in the account on the day I retire will be is $1,268,477.32.

b.Information provided:

Annual withdrawal= $5,500

Time= 32 years

Interest rate= 7%

The question is solved by calculating the future value of ordinary annuity.

Enter the below in a financial calculator to compute the future value of ordinary annuity:

PMT= -5,500

N= 32

I/Y= 7

Press the CPT key and FV to compute the future value of ordinary annuity.

The value obtained is 606,199.85.

Therefore, the amount in the account on the day I retire will be is $606,199.85.

2.Information provided:

Price of the house= $60,000

Present value= $60,000 - $25,000= $35,000

Time= 20 years

Interest rate= 12%

The equal payment is calculated by entering the below in a financial calculator:

PV= -35,000

N= 20

I/Y= 12

Press the CPT key and PMT to compute the equal payment.

The value obtained is 4,685.76.

Therefore, the amount of equal payment is $4,685.76.

3.Information provided:

Future value (PV)= $14,000

Time (N)= 8 years

Interest rate (I/Y)= 14%

The question is solved by first calculating the annual deposit payment.

Enter the below in a financial calculator to compute the annual deposit:

FV= 14,000

N= 8

I/Y= 14

Press the CPT key and PMT to compute the annual deposit.

The value obtained is 1,057.98.

Thereby, the annual deposit is $1,057.98.

4.Information provided:

Present value (PV)= $52,000

Market rate= yield to maturity (I/Y)= 12%/12= 1% per month

Monthly payment= $650

The question is solved by calculating the time of the loan.

Enter the below in a financial calculator to compute the time of the loan:

FV= 52,000

PMT= -650

I/Y= 1

Press the CPT key and N to compute the time of the loan.

The value obtained is 59.0721.

Therefore, the loan is for a period of 59.0721 months.