At what rate percent per annum will ₹ 2000 amount to ₹ 2205 in 2 years compounded annually?

Solution : Given:<br>Principle `(P)=Rs.2000`<br>Amount `(A)=Rs.2315.25`<br>`n=1.5` years means `3` half-years.<br>The rate has to be calculated half-yearly, therefore let `R` be the rate of half-yearly.<br>As we know that,<br>`A=P(1+R/100)^n`<br>`therefore 2315.25=2000(1+R/100)^3`<br>`2315.25/2000=(1+R/100)^3`<br>`231525/2000times100=(1+R/100)^3`<br>`9261/8000=(1+R/100)^3`<br>`(21/20)^3=(1+R/100)^3`<br>`21/20=1+R/100`<br>`21/20-1=R/100`<br>`(21-20)/20=R/100`<br>`1/20=R/100`<br>`R=100/20`<br>`R=5%`.<br>Hence, the rate will be `5%` half yearly and `10%` yearly.

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Solution

Principal (P) = Rs. 2000
Amount (A) = Rs. 2315.25
Period (n) =112 years or 3 half-years.
Let R be a rate of half yearly, then
AP=(1+R100)n
⇒2315.252000=(1+R100)3
231525100×2000=(1+R100)3
⇒231525100×2000=(1+R100)3
⇒92618000=(1+R100)3 (Dividing by 25)
⇒(2120)3=(1+R100)3
Comparing both sides, we get
1+R100=2120=1+120
∴R100=120⇒R=10020=5
∴ Rate =5% half yearly or 10% p.a.

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