Question

I. You are planning to invest $5,000 in a bank which offers you 6% interest P.A. a. Calculate effective annual interest rate(EAR) of this 10-year deposit if interest is compounding on monthly basis. b. How much will be there in your bank account after 10 years, if interest compounding monthly? C. If interest compounding weekly how much more in your account after 10 years? backspace num lock

Answer 1

Solution

1.

Information given,

Investment (P) = $5000

Rate of Interest (r) = 6%, or 0.06

(a)

If, Term of Deposit (n) = 10 Years
and, Number of Compounding, if Monthly (m)= 12

Therefore,
Effective Annual interest rate = (1 + r/m)^m - 1
Or, (1 + 0.06/12)¹² - 1
Or, (1 + 0.005)¹² - 1
Or, (1.005)¹² - 1
Or, 1.0617 - 1 [(1.005)¹² = 1.0617 (Approx.)]
Or, 6.17%

Therefore, the Effective Annual interest rate will be 6.17%.

(b)
Now, the balance will be after 10 years will be calculated as follows (given that amount compounds monthly)
Investment (P) = $5000
Effective rate (R) = 6.17%
Term (n) = 10

So, balance after 10 years will be,
Future Value (F) = P x (1 + R)ⁿ
Or, 5000 x (1 + 0.0617)¹⁰
Or, 5000 x 1.8198 [(1 + 0.0617)¹⁰ = 1.8198 (Approx.)]
Or, 9099

Therefore, the amount will be $9099

(c) Now, if compounding weekly, then Effective rate will be,
(1 + r/m)^m - 1 (As compounding weekly, number of compounding (m) = 52)
Or, (1 + 0.06/52)⁵² - 1
Or, (1 + 0.0012)⁵² - 1
Or, 1.0643 - 1 [(1 + 0.0012)⁵² = 1.0643 (Approx.)]
Or, 6.43%

Now, using this rate, the future value will be = 5000 x (1.0643)¹⁰
Or, 5000 x 1.8648 [(1.0643)¹⁰ = 1.8648 (Approx.)]
Or, 9324

Therefore, if compounding done weekly, balance should be increased by $(9324 - 9099) = $225