A sum of money ₹ 1,640 was borrowed and paid back in two equal instalments. Allowing 5% compound interest find the sum of each instalment.
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A sum of money ₹ 1,640 was borrowed and paid back in two equal instalments. Allowing 5% compound interest find the sum of each instalment.
Answer:
To find the sum of each installment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount paid back (₹ 1,640)
P = the principal amount borrowed (unknown)
r = the annual interest rate (5% or 0.05)
n = the number of times interest is compounded per year (1, since it is compounded annually)
t = the number of years (unknown)
Since the amount is paid back in two equal installments, we can assume that the time period is 1 year for each installment. Therefore, t = 1.
Now, let's solve for P:
₹ 1,640 = P(1 + 0.05/1)^(1*1)
₹ 1,640 = P(1 + 0.05)
₹ 1,640 = P(1.05)
P = ₹ 1,640 / 1.05
P ≈ ₹ 1,561.90
So, the sum of each installment is approximately ₹ 1,561.90.
Step-by-step explanation: