First Simple Bank pays 8 percent simple interest on its investment accounts. If First Complex Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to match First Simple Bank over an investment horizon of 8 years

First Complex Bank should set an interest rate of approximately 6.38% if it wants to match First Simple Bank over an investment horizon of 8 years.

Explanation:

Let us first assume that the amount of the investment is $1.

Simple interest refers to an interest that is calculated based on the principal amount only. The formula for calculating the total amount receivable at the end of the maturity period of an investment under a simple interest is given as follows:

A = P * (1 + rt) ……………. (1)

Where;

A = final amount receivable = ?

P = Principal or investment amount = $1

r = interest rate = 8%, or 0.08

t = time or number of years = 8

Substituting the values into equation (1), we have:

A = $1 * (1 + (0.08 * 8)) = $1.64

Compound interest refers to an interest that is calculated based on the principal amount invested and the interest that accumulates on the amount invested. The formula for calculating the total amount receivable at the end of the maturity period of an investment under a compound interest is given as follows:

A = P * (1 + r)^t ……………. (2)

Where;

A = final amount receivable = $1.64

P = Principal or investment amount = $1

r = interest rate = ?

t = time or number of years = 8

Note that we want to calculate the rate that First Complex Bank should set if it wants to match First Simple Bank over an investment horizon of 8 years. That is why we set it final amount receivable to $1.64 (i.e. A = $1.64) as already obtained under simple interest above. We are now to calculate the annual interest rate.

Substituting the values into equation (2) and solve for r, we have:

1.64 = 1 * (1 + r)^8

1.64 / 1 = (1 + r)^8

1.64 = (1 + r)^8

Taking 8th root of both sides, we have:

1.64^(1/8) = ((1 + r)^8)^(1/8)

1.06378896515711 = 1 + r

r = 1.06378896515711 - 1

r = 0.06378896515711, or 6.378896515711%

Approximating to 2 decimal places, we have:

r = 6.38%

Therefore, First Complex Bank should set an interest rate of approximately 6.38% if it wants to match First Simple Bank over an investment horizon of 8 years.