Question

Brian and Felicia deposit money into separate savings accounts today. Brian deposits X into his account, while Felicia deposits (x/2) . Brian's account earns simple interest at an annual rate of j > 0. Felicia's account earns interest at a nominal annual rate of j, compounded quarterly. Brian and Felicia earn the same amount of interest during the last quarter of the 4th year. Calculate j.

Answer 1

Answer:

Interest earned by Brian during last quarter of 4th year -

Deposit = X, Simple interest at an annual rate of j

Hence, quarterly rate of j/4

So, interest earned in that quarter by Brian will be (X * j/4)/100 = X * j/400 ........................(1)

Now, let's calculate interest earned by Felicia in the same quarter

Deposit = X/2, Compound interest at an annual rate of j, compounded quarterly

Compound interest after 16 quarters (4 years) = (X/2) * (1 + j/400)^16........ (A)

Compound interest after 15 quarters = (X/2) * (1 + j/400)^15................(B)

Hence, Compound interest earned in the 4th quarter of 4th year = A - B

= (X/2) * (1 + j/400)^15 * (j/400)............................................................................................(2)

As per given information, equating (1) and (2),

2 = (1 + j/400)^15

Solving this, we get j = 18.92%