Question

Arif took a loan at the interest of 10% per annum. Find the difference in amounts he would be paying after 1 and the half year of the interest is compounded half yearly​

Answer 1

Answer:

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Step-by-step explanation:

Given,

Principal amount, P = Rs 80000

Rate of interest, R = 10% p.a.

Time period = 1\frac{1}{2} years.

We know, Amount when interest is compounded annually, A =

A =P(1+\frac{R}{100})^n

Now, For the first year, A=

A =80000(1+\frac{10}{100})^1= Rs. 88000

For the next half year, this will act as the principal amount.

\therefore Interest for 1/2 year at 10% p.a =

=\frac{88000\times\frac{1}{2}\times10}{100}= Rs 4400

Required total amount = Rs (88000 + 4400) = Rs 92400

(ii) If it is compounded half yearly, then there are 3 half years in 1\frac{1}{2} years.

\therefore n = 3 half years.

And, Rate of interest = half of 10% p.a = 5% half yearly

\therefore A =80000(1+\frac{5}{100})^3= Rs.\: 92610

\therefore The difference in the two amounts = Rs (92610 - 92400) = Rs 210