Question

Find the least number of years for which an annuity of Rs. 1,000 must run in order that its amount exceed Rs. 16,000 at 5% p.a. compounded monthly.
[Given : Log 18 = 1.2553, log 105 = 2.8212]

• A. 12 years
• B. 11 years
• C. 13 years
• D. None.

Answer 1

The correct option is C 13 years

$F=R\frac{{(1+\frac{r}{m})}^{m\times n}-1}{\frac{r}{m}}$

$16000=1000\frac{{(1+\frac{5}{100})}^n-1}{\frac{5}{100}}$

$16=1\frac{{(1+\frac{5}{100})}^n-1}{\frac{5}{100}}$

$0.8=(1.05{)}^n-1$

$1.8=(1.05{)}^n$

Applying log on both sides, we get,

$\log 1.8=n\log 1.05$

$\Rightarrow n=13$

Least number of years = $13$ years