Question

In what time will Rs 8000 at 5% per annum compounded annually will amount to rupees 8820

Answer 1

Principal = Rs 8000

Interest rate = 5%

Amount Received = Rs 8820

Find the time needed:

Amount = P(1 + r)ⁿ

8820 = 8000( 1 + 0.05)ⁿ

8820 = 8000(1.05)ⁿ

1.05ⁿ = 1.1025

log 1.05ⁿ = log 1.1025

n log 1.05 =  log 1.1025

n = log 1.1025 ÷  log 1.05

n = 2

Answer: It will take 2 years

Answer 2

$\underline{\bold{Given:-}}$

Principal = 8000 rupees

Compound interest = 5% per annum

$\underline{\bold{Solution:-}}$

Let, it will take x years to amount to 8820 rupees.

Amount = 8820 rupees

$P {(1 + \frac{5}{100}) }^{n} = 8820 \\ \\ 8000 {( \frac{105}{100} )}^{n} = 8820 \\ \\ {( \frac{21}{20} )}^{n } = \frac{8820}{8000}$

${(1.05)}^{n} = 1.025 \\ \\ {(1.05)}^{n} ={(1.05)}^{2} \\ \\ On \: comparing \: there \: powers \\ \\ n = 2$

So, in 2 years the amount will become 8820 rupees.