Question

A sum of 10,000 yields 3310 as compound interest in 3 years.
If interest is compounded yearly, find the:
(i) amount

2.rate of interest​

Answer 1

The amount is Rs 13310 and rate of interest is 10 % per annum

Solution:

Given that,

A sum of 10,000 yields 3310 as compound interest in 3 years

Principal = 10, 000

Compound interest = 3310

Find the amount

Amount = Principal + Compound interest

Amount = 10000 + 3310

Amount = 13310

Find the rate of interest

The amount when interest is compounded yearly is given as:

$A = p(1+\frac{r}{100})^t$

Where,

p is the principal

r is the rate of interest

t is number of years

$13310= 10000(1 + \frac{r}{100})^3\\\\\frac{13310}{10000} = ( \frac{100+r}{100})^3\\\\\frac{1331}{1000} = ( \frac{100+r}{100})^3\\\\\(\frac{11}{10})^3 = ( \frac{100+r}{100})^3\\\\Powers\ are\ same\ therefore\\\\\frac{11}{10} = \frac{100+r}{100}\\\\110 = 100 + r\\\\r = 10$

Thus rate of interest is 10 % per annum

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