Question

the difference between the compound and simple interest on certain sum of money at 15% pa for 3 years is 283.50rs. find the sum.

Answer 1

The sum is 401 rupees.

Explanantion:

Total compounded interest = P (1 + r/n) (nt) + P

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested or borrowed for

Compound Interest (C) = P (1 + r/n) (nt) - P = P(1+ 0.15/1) (1 x 3) - P

Simple interest (S) = P(1+ rt)

The difference between the compound and simple interest = P(1+ 0.15/1) ^(1 x 3) + P - (P + Prt)

= P(1+ 0.15/1) ^(1 x 3) - Prt)

= P (1+ 3/20) ^ 3 - P  (0.15 x 3)

= P ( 1+ 3/20) ^ 3 - 0.45)

Now: P ( 1+ 3/20) ^ 3 - 0.45) = 283.50

=> P = 283.50/ ( 23/20) ^ 3 - 1.45)

=> P = 283.50/(1.157625-.45)

=> P = 283.50/0.707625

=> P = 400.64