Question

Please help... Chan deposited money into his retirement account that is compounded annually at an interest rate of 7%.

Chan thought the equivalent quarterly interest rate would be 2%. Is Chan correct? If he is, explain why. If he
is not correct, state whats the equivalent quarterly interest rate is and show how you got your answer.

Answer 1

r = 1.7 percent

Explanation:

I = P(1+r)^nt

assuming the principal is the same

yearly

I = (1 +.07)^1

quarterly

I = (1+ r) ^4t

lets find the quarterly interest rate if we get the same interest

(set the equations equal)

(1 +.07)^1= (1+ r) ^4

simplify

1.07 = (1+r) ^4

take the 4th root on each side

(1.07) ^ (1/4) = (1+r) ^ 4 ^ (1/4)

1.017058525 = 1+r/4

subtract 1

.017058525 = r

multiply by 100

r = 1.7 percent