Varun took a loan of ruppees 80,000 from a bank. If the rate of interest is 10 percent per annum find the difference in amounts he would be paying after 1 1/2 years if the interest is
compounded annually
compounded half yearly
Answers
Solution :
Compounded annually
- P = Rs 80,000
- R = 10% per annum
- n = 1½ year
the amount for 1 year and 6 months can be calculated by first calculating the amount for year using the compound interest formula, and then calculating the simple interest for 6 months on the amount obtained at the end of 1 year.
First, the amount for 1 year has to be calculated.
Amount, A = P(1 + R/100)^n
=80000 (1 + 10/100)¹
= 80000 x 11/100
= Rs 88000
By taking 88,000 as principal, the Sl for the next ½ year wil be calculated.
I = P x R x T/100
= 88000 x 10 x ½/100
= Rs 4400
Interest for the first year = Rs 88000 - Rs 80000 = Rs 8,000
And interest for the next ½ year = Rs 74,400
Total C.I. = 8000 + 4,400 +
= Rs 12400
A = P + C.l
= Rs (80000 + 12400)
= Rs 92,400
The interest is compounded halt yearly.
Rate = 10% per annum = 5% per halfyear
There will be three half years in 1 ½ years.
Amount, A = P(1 + R/100)^n
=Rs 80000(1 + 10/100)^³
= Rs 80000 x (105/100)³
= Rs 92610
Difference between the amounts
= Rs 92,610 - Rs 92,400
= Rs 210