Question : Find the amount (integral value only) if a sum of INR 6,500 is being borrowed at 10% interest per annum for 2 years if interest is compounded half-yearly.
Option 1: INR 8,150
Option 2: INR 7,900
Option 3: INR 7,650
Option 4: INR 8,250
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Correct Answer: INR 7,900
Solution :
Here, principal = INR 6,500
Rate compounded half-yearly = $\frac{10}{2}=5\%$
Time = 2 × 2 = 4 years as it compounded half-yearly
We know, Total amount = $P(1+\frac{r}{100})^{n}$, where $P$ = Principal, $r$ = Rate of interest, $n$ = Time
⇒ Total amount = $6500(1+\frac{5}{100})^4$
⇒ Total amount = $6500(\frac{21}{20})^4$
⇒ Total amount = $6500×\frac{441}{400}×\frac{441}{400}$
⇒ Total amount = $7900.79\approx 7900$
Hence, the correct answer is INR 7900.
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