Question

Jack deposited $500,000 into a bank for 6 months. At the end of that time, he withdrew the money and received $520,000. If the bank paid interest based on continuous compounding:
a. What was the effective annual interest rate?
b. What was the nominal annual interest rate?

Answer 1

$18\%$ compounded monthly

(a)

– interest rate per month: i =$18\%/12 = 1.5\%$

– no. interest periods per year:$N = 12$

Suppose that you invest $500,000 for 6 months at 18% compounded monthly.

$F= \$500,000 (1 + i)^N = \$500,000(1 + 0.015)^{12}$

$= \$1,195.60$

$i = 0.1956——>19.56\%$

(b)

Nominal Rate per Period:

r = 59.437024%

Rate per Compounding Intereval:

p = 92.5728374%