Karan took a loan of rs 70000 from a bank. If the rate of interest is 10%per annum find difference in amount he would be paying after 1.5 year if the interest is compound annually and compound half yearly
compound: 70000(1+.10/2)^3 = 81033.75
simple: 70000(1+(.10/2)*3) = 80500
oops. I misread. the problem.
The above rates are for 1/2 yearly accrual of interest.
For annual compounding, the amount is
70000(1+.10)^(3/2) = 80758.28
Actually, though, after a year and a half, the annual rate has only been applied once, so the amount in the account is only
70000(1+.10)^1 = 77000
The interest will not be applied till the end of the 2nd year.
To find the difference in the amount Karan would be paying after 1.5 years with compound annual interest and compound half-yearly interest, we need to use the compound interest formula:
Compound Interest = Principal Amount * (1 + Rate/100)^Time - Principal Amount
1. Compound Annual Interest:
First, let's calculate the amount Karan would be paying after 1.5 years with compound interest compounded annually:
Principal Amount = Rs 70,000
Rate of Interest = 10% per annum
Time = 1.5 years
Compound Interest = 70000 * (1 + 10/100)^1.5 - 70000
To get the difference in the amount from the original principal, we subtract the principal amount from the compound interest:
Difference = Compound Interest - Principal Amount
2. Compound Half-Yearly Interest:
Now, let's calculate the amount Karan would be paying after 1.5 years with compound interest compounded half-yearly. Here, the time is in half-yearly terms, so we need to adjust the rate accordingly:
Principal Amount = Rs 70,000
Rate of Interest = 10% per annum = 5% per half year (10%/2)
Time = 1.5 years = 3 half years (1.5 * 2)
Compound Interest = 70000 * (1 + 5/100)^3 - 70000
Again, to get the difference in the amount from the original principal, we subtract the principal amount from the compound interest:
Difference = Compound Interest - Principal Amount
By calculating the differences using these formulas, you will find the respective differences in the amounts for compound annual and compound half-yearly interest.