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प्रश्न
Rahim borrowed Rs 10,24,000 from a bank for one year. If the bank charges interest of 5% per annum, compounded half-yearly, what amount will he have to pay after the given time period. Also, find the interest paid by him.
उत्तर
Given, Amount borrowed by Rahim (P) = 1024000 with a time period (T) = 1 yr.
Also, Rate of interest (R) = 5% per annum compounded half-yearly.
Let Amount = A
Now, for interest compounded half-yearly
`A = P(1 + (R/n))^(2T)`
⇒ `A = 1024000(1 + (5/200))^(2(1))`
Since, In half-yearly `R = R/2` and T = 2T
⇒ `A = 1024000(1 + (5/200))^2`
= `1024000 (1 + (1/40))^2`
= `1024000(41/40)^2`
= `1024000 xx (41/40) xx (41/40)`
= 640 × 41 × 41
= Rs. 1075840
Now, we know compound interest, CI = Amount – Principle
⇒ CI = 1075840 – 1024000
= Rs. 51840
Hence, interest paid by him is Rs. 51840.
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