Question

Compute the effective annual rate of interest

a) for 6% compounded monthly

b) at which $1100 will grow to $2000 in seven years if compounded monthly

Answer 1

a) For 6% compounded monthly

The annual interest rate is i = 6% but it is compounded monthly (12 months in a year), therefore

Effective annual interest rate = (1+ i/12) ^12 -1

= (1+ 6%/12) ^12 -1

= (1+0.06/12) ^12 -1

= 0.0617 or 6.17% per annum

b) At which $1100 will grow to $2000 in seven years if compounded monthly

The monthly interest rate can be calculated with the help of following formula

Present value (PV) of money = FV / (1+ i) ^n

Where,

Present value (PV) of money =$1100

Future value (FV) of money = $2,000

Assume that Annual rate of interest is I and compounded monthly, therefore monthly interest rate is I/12 =i

And time period n = 7 years or 7 * 12 = 84 months

Therefore,

$1100 = $2,000 / (1+i %) ^84

OR i = 0.714% per month

Effective annual interest rate = (1+ 0.714%) ^12 -1

= (1+ 0.00714) ^12 -1

= 0.0892 or 8.92% per annum