Question

Calculate the future value in five years of $5,000 received today if your investments pay a. 6 percent compounded annually b. 8 percent compounded annually c. 9 percent compounded annually d. 9 percent compounded semiannually e. 9 percent compounded quarterly What do your answers to these questions tell you about the relation between future values and interest rates and between future values and the number of compounding periods per year? (LG 2-9)

Answer 1

a.Information provided:

Present value= $5,000

Time= 5 years

Yield to maturity= 6%

The question is calculated by computing the future value.

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

PV= -5,000

I/Y= 6

N= 5

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

The value obtained is 6,691.13.

Therefore, the future of the investment is $6,691.13.

b.Information provided:

Present value= $5,000

Time= 5 years

Yield to maturity= 8%

The question is calculated by computing the future value.

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

PV= -5,000

I/Y= 8

N= 5

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

The value obtained is 7,346.64.

Therefore, the future of the investment is $7,346.64.

c.Information provided:

Present value= $5,000

Time= 5 years

Yield to maturity= 9%

The question is calculated by computing the future value.

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

PV= -5,000

I/Y= 9

N= 5

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

The value obtained is 7,693.12.

Therefore, the future of the investment is $7,693.12.

d.Information provided:

Present value= $5,000

Time= 5 years*2= 10 semi-annual periods

Yield to maturity= 9%/2= 4.5% per semi-annual period

The question is calculated by computing the future value.

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

PV= -5,000

I/Y= 4.50

N= 10

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

The value obtained is 7,764.47.

Therefore, the future of the investment is $7,764.47.

e.Information provided:

Present value= $5,000

Time= 5 years*4= 20 quarters

Yield to maturity= 9%/4= 2.25% per quarter

The question is calculated by computing the future value.

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

PV= -5,000

I/Y= 2.25

N= 20

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

The value obtained is 7,802.55.

Therefore, the future of the investment is $7,802.55.

Interest rates and future value have a direct relationship. The higher the interest rate, the higher the future value and vice-versa.

Future values and number of compounding periods per year also have a direct relationship. The more number of compounding periods per year, the higher the future value and vice-versa.

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