Question

Ex2: You invest $1000 in an account that pays 5% per year compounded quarterly.a. Write a compound interest model that would be used to determine the future value of the investment after + years.b. How much will you have in the account after 3 years if you make no further deposits?C. The APY (annual percent yield) is the rate of interest earned for the simple interest equivalent of the model determined above. What is the APy for this model?

Answer 1

Hello there. To solve this question, we'll have to remember how to calculate the future value of an compound interest.

a). To write this compound interest model, remember that given the present value is P, the yearly interest rate is i and it is compounded n times in a year, the formula is:

FV = P * (1 + i/n)^(nt)

Plugging in P = 1000, i = 5% or 0.05 (after converting to decimals), n = 4, we have that:

FV = 1000 * (1 + 0.05/4)^(4t) = 1000 * (1.0125)^(4t)

b) How much will you have in the account after 3 years if you make no further deposits? In this case, the present value will not change and we'll have t = 3:

FV = 1000 * 1.0125^(4*3) = 1000 * 1.0125^(12) = 1160.75

c). To determine the APY, we use the formula:

APY = (1 + i/n)^n - 1

Thus we have:

APY = (1 + 0.05/4)^4 - 1 = 1.0125^4 - 1 = 0.051