Question

A sum of $Rs.1000$ is deposited every year at $8$% simple interest. Calculate the interest at the end of each year. Do these interest amounts form an A.P.? If so, find the total interest at the end of $30$ years

Answer 1

We know that the formula to find the simple interest with the principal amount $P$, rate of interest $R$ and time $T$ is:

$S.I=\frac{P\times R\times T}{100}$

It is given that a sum of Rs. $1000$ is deposited every year at $8$% simple interest, therefore,

$S.I=\frac{1000\times 8\times 1}{100}=\frac{8000}{100}=80$

Therefore, the interest amounts beginning from the first year are $80,160,240,....$

The above sequence is an arithmetic progression. From this we have to find the sum of $30$ terms because we have to find the interest amount for $30$ years.

We know that the sum of an arithmetic series with first term $a$ and common difference $d$ is $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$, therefore, with $a=80,d=160-80=80$ and $n=30$, we have

$S_{30}=\frac{30}{2}\left[\right(2\times 80)+(30-1\left)80\right]=15[160+(29\times 80\left)\right]=15(160+2320)=15\times 2480=37200$

Hence, the total interest at the end of $30$ years is $37200$.