Question

6. Ariftook a loan of 180.000 from a bank. If the rate of interest is 10% per ann
find the difference in amounts he would be paying after
(1) after 1 year?
compounded annually
(ii) compounded half yearly.​

Answer 1

Answer:

Rs. 92400 , Rs. 210

Step-by-step explanation:

Given,

Principal amount, P = Rs 80000

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

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

(i)

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

Hope it helps :)