Rs. 5,000 is borrowed at 8% for 1 $\frac{1}{2}$ years. Calculate the compound interest being compounded semi annually (half-yearly). What would have been the interest earned if the same amount was borrowed for simple interest at the same rate for the same duration?

Open in App

Solution

Principal = Rs. 5,000, time = 1 $\frac{1}{2}$ years = 3 half years, i.e., T = $\frac{1}{2}$ and has to be used three times, and R = 8%.
Interest for the first half year (using simple interest formula) $= \frac{5000 \times 1 \times 8}{2 \times 100}$ = Rs. 200.
Principal for the second half year = Rs. 5,000 + Rs. 200 = Rs. 5,200.
Interest for the second half year = $\frac{5200 \times 1 \times 8}{2 \times 100} = R s . 208$ .
Principal for the third half year = Rs. 5,200 + Rs. 208 = Rs. 5,408.
Interest for the third half year = $\frac{5, 408 \times 1 \times 8}{2 \times 100} = R s . 216.32$
Therefore, amount = Rs. 5,408 + Rs. 216.32 = Rs. 5,624.32
Compound interest = amount - principal = Rs. 5,624.32 - Rs. 5,000 = Rs. 624.32
Simple interest for Rs. 5,000 for 1 $\frac{1}{2}$ years at the rate of 8% $= \frac{5000 \times 8 \times 3}{100 \times 2} = R s . 600$

Suggest Corrections

Similar questions

R s . 20, 000

is lent for

2

years at

5 %

compound interest. Calculate the compound interest and the amount after

2

years if the interest is compounded annually. What would have been the interest earned if the same amount was lent for simple interest at the same rate for the same duration?

The interest earned on $R s . 20000$ at the rate of $20 %$ per annum for $1.5$ years if compounded semi annually is how much more than the simple interest earned on the same amount with the same rate of interest for the same period.

Q. An industrialist borrowed the

R s 75, 000

for two years at the rate

2.5 %

p.a.compounded annually. Calculate the total amount compound interest by simple interest method.

Q. Sunitabai borrowed Rs 60,000 at 9 p.c.p.a simple interest for 3 years to have her house repaired. Had she borrowed the same sum for the same period and the same rate at compound interest, how much more interest would she have had to pay?

Q. Ganesh invested Rs 40,000 in a bank at 8 p.c.p.a compound interest for 2 years. What would be the difference in the interest earned if he invests the same amount for the same period but for simple interest at the same rate?

Join BYJU'S Learning Program

Rs. 5,000 is borrowed at 8% for 112 years. Calculate the compound interest being compounded semi annually (half-yearly). What would have been the interest earned if the same amount was borrowed for simple interest at the same rate for the same duration?

Rs. 5,000 is borrowed at 8% for 1 $\frac{1}{2}$ years. Calculate the compound interest being compounded semi annually (half-yearly). What would have been the interest earned if the same amount was borrowed for simple interest at the same rate for the same duration?