What's the answer?

Question

~~A debt of $200 is due in six months if the rate of interest is 15%. What is the value of the debt if it is paid
a)two month hence?
b)six month hence?
c)nine month hence?

Answer 1

Assuming simple interest of 15% per annum, this is the same as 15/12=1.25% monthly. This comes to 200×1.25/100=$2.50 each month.

a) 2 months’ interest is 2×2.50=$5 so the debt is $205 including interest.

b) 6 months’ interest is 6×2.50=$15 so the debt is $215.

c) 9 months’ interest is 9×2.50=$22.50 making the debt $222.50.

But the debt was due with interest after 6 months when it had reached $215. So we may need to consider an effective new loan starting after 6 months. That means working out the interest on $215 for 3 months. The interest per month on $215 is 1.25×215/100=$2.6875. So for 3 months this will come to about $8.06 making the total debt $223.06.