Question

6a. Suppose your bank pays you 1% interest on your savings account every three months. What is your compound annual interest rate?

b. Suppose you have an investment which doubled in value in four years. What is your compound annual rate of return?

Answer 1

A). Compound interest formula :

Compound interest = Principal * ( 1+r /100) ^ N - Principal,

r = 1% quarterly i.e every three months, N = 4 because there are 4 quarters in a year, Assuming principal = 1, we get

Compound Interest = 1 * (1 + 1/100) ^ 4 - 1 = (1.01)^4 - 1 = 1.0406 - 1 = 0.406 = 4.06%

Compound Interest = 4.06%

B). In this question we will use the below formula,

Amount = Principal * (1 + r / 100) ^ n

Assuming principal = 1, our amount became 2 in four years as mentioned in the question,

2 = 1 * (1+r /100) ^ 4

2 ^1/4 = 1+ r /100

1.1892 = 1 +r /100

r = 18.92%

Compound annual rate of return is 18.92%.