Question

John has just been notified that the combined principal and interest on an amount that he borrowed 36 months ago at 11% compounded semi annually is now $3800, how much is interest?

Answer 1

Note that interest is given for 1 year which is compounded semi-annually. So we have to convert it into semi-annual interest, i.e interest for 6 months. Therefore, the interest rate for 6 months is 11% / 2 = 5.5%

And time is given in months, when the compounding is semi-annually, frequency of compounding happens in a period of 6 months. So number of compounding in 36 months = 36 / 6 = 6 periods.

Step 1: Find the principal amount:

Where,
P = Principal amount
A = Final amount
i = Interest rate per period (i.e for six months 5.5%)
n = Total number of compounding (6 periods)

Therefore,

Step 2: Find the interest by subtracting principal amount(P) from final amount (A):

Interest = Final Amount - Principal amount

= $3,800.00 -  $2,755.93

= $1,044.07