Question

1.) Find the interest rates earned on each of the following. Round your answers to the nearest whole number.

1. You borrow $99,000 and promise to pay back $307,479 at the end of 10 years.

     %

2. You borrow $9,000 and promise to make payments of $2,684.80 at the end of each year for 5 years.

     %

2.) Your client is 33 years old. She wants to begin saving for retirement, with the first payment to come one year from now. She can save $8,000 per year, and you advise her to invest it in the stock market, which you expect to provide an average return of 12% in the future.

1. If she follows your advice, how much money will she have at 65? Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

2. How much will she have at 70? Do not round intermediate calculations. Round your answer to the nearest cent.

   $  

3. She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If her investments continue to earn the same rate, how much will she be able to withdraw at the end of each year after retirement at each retirement age? Do not round intermediate calculations. Round your answers to the nearest cent.

   Annual withdrawals if she retires at 65: $

   Annual withdrawals if she retires at 70: $

Answer 1

1.i.Information provided:

Present value= $99,000

Future value= $307,479

Time= 10 years.

The question is solved by calculating the yield to maturity.

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 307,479

PV= -99,000

N= 10

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 12.

Therefore, the interest rate is 12%.

iiInformation provided:

Present value= $9,000

Annual payment= $2,684.80

Time= 5 years.

The question is solved by calculating the yield to maturity.

The yield to maturity is calculated by entering the below in a financial calculator:

PV= -9,000

PMT= 2,684.80

N= 5

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 14.9994.

Therefore, the interest rate is 15%.

2.i.Information provided:

Annual saving= $8,000

Time= 65 years - 33 years= 32 years

Interest rate= 12%

The question is solved by calculating the future value.

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

PMT= -8,000

N= 32

I/Y= 12

Press the CPT key and FV to compute the future value.

The value obtained is 2,438,781.75.

Therefore, my client had saved $2,438,781.75 at age 65.

2.ii.Information provided:

Annual saving= $8,000

Time= 70 years - 33 years= 37 years

Yield to maturity= 12%

The question is solved by calculating the future value.

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

PMT= -8,000

N= 37

I/Y= 12

Press the CPT key and FV to compute the future value.

The value obtained is 4,348,789.52.

Therefore, my client will have $4,348,789.52 at 70.

3.i. Information provided:

Present value= $2,438,781.75

Time= 20 years

Yield to maturity= 12%

The annual withdrawal at age 65 is calculated by entering the below in a financial calculator:

PV= -2,438,781.75

N= 20

I/Y= 12

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

The value obtained is 326,501.13.

Therefore, the annual withdrawal at age 65 is $326,501.13.

3.ii.Information provided:

Present value= $4,348,789.52

Time= 15 years

Yield to maturity= 12%

The annual withdrawal at age 65 is calculated by entering the below in a financial calculator:

PV= -4,348,789.52

N= 15

I/Y= 12

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

The value obtained is 638,507.71.

Therefore, the annual withdrawal at age 70 is $638,507.71.

In case of any query, kindly comment on the solution.