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PROBLEM 5-3 COMPOUND VALUE SOLVING FOR ANNUAL RATE At what annual rate would the following lump...

PROBLEM 5-3
COMPOUND VALUE SOLVING FOR ANNUAL RATE

At what annual rate would the following lump sums have to be invested to reach the future values shown? a. $500 to grow to $1,948.00 in 12 years b. $300 to grow to $422.10 in 7 years c. $50 to grow to $280.20 in 20 years d. $200 to grow to $497.60 in 5 years

SOLUTION
a. $500 to grow to $1,948.00 in 12 years
Invest	$500.00
Future value	$1,948.00
Number of years	12
Annual rate

b. $300 to grow to $422.10 in 7 years
Invest	$300.00
Future value	$422.10
Number of years	7
Annual rate

c. $50 to grow to $280.20 in 20 years
Invest	$50.00
Future value	$280.20
Number of years	20
Annual rate

d. $200 to grow to $497.60 in 5 years
Invest	$200.00
Future value	$497.60
Number of years	5
Annual rate

Requirements:

Solutions

Expert Solution

a.Information provided:

Present value= 500

Future value= $1,948

Time= 12 years

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

PV= -500

FV= 1,948

N= 12

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

The value obtained is 12.14.

Therefore, the interest rate is 12.14%.

b. Information provided:

Present value= $300

Future value= $422.10

Time= 7 years

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

PV= -300

FV= 422.10

N= 7

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

The value obtained is 4.9989

Therefore, the interest rate is 4.9989% $\rightarrow$ 5%.

c. Information provided:

Present value= 50

Future value= $280.20

Time= 20 years

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

PV= -50

FV= 280.20

N= 20

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

The value obtained is 8.9996.

Therefore, the interest rate is 8.9996% $\rightarrow$ 9%.

d. Information provided:

Present value= 200

Future value= $497.60

Time= 5 years

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

PV= -200

FV= 497.60

N= 5

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

The value obtained is 19.9969

Therefore, the interest rate is 19.9969% $\rightarrow$ 20%.

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

jeff jeffy answered 4 months ago

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