Question

Derek can deposit $266.00 per month for the next 10 years into an account at Bank A. The first deposit will be made next month. Bank A pays 12.00% and compounds interest monthly. Derek can deposit $2,572.00 per year for the next 10 years into an account at Bank B. The first deposit will be made next year. Bank B compounds interest annually. What rate must Bank B pay for Derek to have the same amount in both accounts after 10 years?

Answer 1

Bank A

Deposit per month by Derek =$266

Number of months of deposit(n) =10*12 =120

Rate per month =12%/12 =1%

 

Explanation:

Amount in Bank A after 10 years has been calculated using FV of annuity formula.

 

Bank B

Number of Years(n) =10

Deposit per Year =$2572

FV in Bank B is same as Bank A =61,190.2914

 

Rate has been calculated using excel formula

	A	B
1	Deposit per year	$2,572
2	Number of years	10
3	Value in year 10(FV)	61,190.29
4	Rate	18.2316%
	Excel Formula	RATE(B2,B1,0,-B3)

Explanation:

Annual rate has been calculated using rate function of excel.

 

Rate Bank B must pay for Derek to have the same amount in both accounts after 10 years =18.23%.

Rate Bank B must pay for Derek to have the same amount in both accounts after 10 years =18.23%.