Question

Calculate the following time value of money problems:

1. If you want to accumulate $500,000 in 20 years, how much do you need to deposit today that pays an interest rate of 15%?
2. What is the future value if you plan to invest $200,000 for 5 years and the interest rate is 5%?
3. What is the interest rate for an initial investment of $100,000 to grow to $300,000 in 10 years?
4. If your company purchases an annuity that will pay $50,000/year for 10 years at a 11% discount rate, what is the value of the annuity on the purchase date if the first annuity payment is made on the date of purchase?
5. What is the rate of return required to accumulate $400,000 if you invest $10,000 per year for 20 years. Assume all payments are made at the end of the period.

Answer 1

1. Information provided:

Future value= $500,000

Time= 20 years

Interest rate= 15%

The question is concerning finding the present value of an annuity due. Annuity due refers to annuity that occurs at the beginning of a period.

This can also be solved using a financial calculator by inputting the below into the calculator:

The financial calculator is set in the end mode. Annuity due is calculated by setting the calculator to the beginning mode (BGN). To do this, press 2^nd BGN 2^nd SET on the Texas BA II Plus calculator.

Enter the below in a financial calculator in BGN mode:

FV= 500,000

N= 20

I/Y= 15

Press the CPT key and PV to compute the present value.

The value obtained is 30,550.14.

Therefore, $30,550.14 must be deposited today.

2. Information provided:

Yearly investment= $200,000

Time= 5 years

Interest rate= 5%

The future value is calculated by entering the below in a financial calculator:

PMT= 200,000

N= 5

I/Y= 5

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

The value obtained is 1,105,126.25.

Therefore, the future value is $1,105,126.25.

3. Information provided:

Present value= $100,000

Future value= $300,000

Time= 10 years

The interest rate is calculated by entering the below in a financial calculator:

PV= -100,000

FV= 300,000

N= 10

Press the CPT key and I/Y to compute the interest rate.

The value obtained is 11.61.

Therefore, the interest rate is 11.61%.

4. Information provided:

Annuity= $50,000

Time= 10 years

Interest rate= 11%

The question is concerning finding the present value of an annuity due. Annuity due refers to annuity that occurs at the beginning of a period.

This can also be solved using a financial calculator by inputting the below into the calculator:

The financial calculator is set in the end mode. Annuity due is calculated by setting the calculator to the beginning mode (BGN). To do this, press 2^nd BGN 2^nd SET on the Texas BA II Plus calculator.

Enter the below in a financial calculator in BGN mode:

PMT= 50,000

N= 10

I/Y= 11

Press the CPT key and PV to compute the present value.

The value obtained is 326,852.38.

Therefore, the value of the annuity on the purchase date is $326,852.38.

5. Information provided:

Future value= $400,000

Annuity= $10,000

Time= 20 years

The rate of return is calculated by entering the below in a financial calculator:

FV= 400,000

PMT= 10,000

N= 20

Press the CPT key and I/Y to compute the rate of return.

The value obtained is 6.77.

Therefore, the rate of return is 6.77%.

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