3) Amit took a loan of Rs. 80,000 from a bank. If the rate of interest is 10% per annum find the difference in amounts he would be paying after 1 1 2 years if the interest is a) Compounded annually. b) Compounded half yearly.
Answers
Answer: (i) Given,
Principal amount, P = Rs80000
Rate of interest, R = 10% p.a.
Time period = 1 and a half years.
We know, Amount when interest is compounded annually, A =
A = P(1 + R/100)^n
Now, For the first year, A =
A = 80000(1 + 10/100)^1 = Rs88000
For the next half year, this will act as the principal amount.
therefore Interest for 1/2 year at 10% p.a =
= (88000 x 1/2 x 10)/100 = Rs4400
Required total amount = Rs (88000 + 4400) = Rs92400
(ii) If it is compounded half yearly, then there are 3 half years in 1 and a half years.
therefore n = 3 half years.
And, Rate of interest = half of 10% p.a = 5% half yearly
therefore A = 80000 (1 +5/100)^3 = Rs92610
therefore The difference in the two amounts = Rs (92610 - 92400) = Rs 210
Step-by-step explanation: