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A sum put out at 4% compound interest payable half yearly amounts to Rs 13265.10 in 11/2 years. Find the sum.
The formula for annual compound interest, including principal sum, is:A = P (1 + r/n) (nt)Where:A = the future value of the investment/loan, including interestP = the principal investment amount (the initial deposit or loan amount)r = the annual interest rate (decimal)n = the number of times that interest is compounded per yeart = the number of years the money is invested or borrowed forNow according to your questionA = 13265.10 Rs.t = 11/2 yearr = 4%n = 2 (as, half yearly)Therefore, 13265.10=P(1+4/(2×100))2×11/2Or, 13265.1= P(51/50)11Or, P=13265.1(50/51)11Or, P = 10668.62 (approx.)Therefore the sum of the amount was Rs. 10668.62 (approx.)
The formula for annual compound interest, including principal sum, is:A = P (1 + r/n) (nt)
Where:
A = the future value of the investment/loan, including interestP = the principal investment amount (the initial deposit or loan amount)r = the annual interest rate (decimal)n = the number of times that interest is compounded per yeart = the number of years the money is invested or borrowed for
Now according to your question
A = 13265.10 Rs.
t = 11/2 year
r = 4%
n = 2 (as, half yearly)
Therefore, 13265.10=P(1+4/(2×100))2×11/2
Or, 13265.1= P(51/50)11
Or, P=13265.1(50/51)11
Or, P = 10668.62 (approx.)
Therefore the sum of the amount was Rs. 10668.62 (approx.)
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