Question

At what rate percent will a sum of rupees 5000 produce rupees 408 as compound interest at 5% per annum?

Answer 1

After 1.6 years, the amount will produce 408 as compound interest.

Step-by-step explanation:

Consider the correct question is,

At what time will a sum of rupees 5000 produce rupees 408 as compound interest at 5% per annum?

Since, the compound interest formula is,

$I=P(1+\frac{r}{n})^t-P$

Where,

P = principal amount,

r = annual rate of interest,

t = number of years,

n = number of compounding periods,

Here, P = 5000, I = 408, r = 5% = 0.05, n = 1,

By substituting the values,

$408=5000(1+0.05)^t - 5000$

$408=5000(1.05^t-1)$

$\frac{408}{5000}=1.05^t-1$

$0.0816=1.05^t-1$

$1.0816=1.05^t$

Taking ln both sides,

$\ln(1.0816)=t\ln(1.05)$

$\implies t =\frac{\ln(1.0816)}{\ln(1.05)}\approx 1.6$

Hence, after 1.6 years, the amount will produce 408 as compound interest.

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Answer 2

Answer:

Answer = time=1.6, rate = 4%