Compound Inverse problems

We have already learnt the formula, where four variables A, P, r and n are involved. Out of these four variables, if any three variables are known, then we can calculate the fourth variable.

when interest is being compounded annually? Example 1: At what rate per annum will Rs. 640 amount to Rs.774.40 in 2 years, when interest is being compounded annually? Solution: Given: P = Rs. 640, A = Rs.774.40, n = 2 years To Find: Rate(r) We know, To remove decimal point from the numerator, we multiply both numerator and denominator by 100 774.40 = 774.40 x 100 =77440 640=640 x 100 = 64000 121 968 800 100

121 = 11 x 11 100 = 10 x 10 since powers are same we compare the base Ans:- Rate r = 10% per annum

per annum compound interest. Example 2 : In how much time will a sum of Rs.1600 amount to Rs.1852.20 at 5% per annum compound interest. Solution Given: P = Rs. 1600, A = Rs. 1852.20, r = 5% per annum To Find :- No of years(n) We know 21 To remove decimal point from the numerator, we multiply both numerator and denominator by 100 1852.20 = 1852.20 x 100 =185220 160=160 x 100 = 16000 20 9261 8000

Ans:- No of years is 3 years 9261 = 21 x 21 x 21 8000 = 10 x 10 x 10 since bases are same we compare the powers ∴ n= 3 years Ans:- No of years is 3 years

Try these In how much time will a sum of Rs.400 amount to Rs. 529 at 15 % per annum compound interest.