Question

Ramakant wants to earn rs.1,500 interest on his deposits. He plans to buy a sack of grains with the interest. He puts rs.5,000 into his account that earns 2.5% interest. How long will he need to leave his money in the account to earn this interest that would help him buy the sack of grains?

Answer 1

Answer:

10.625 years

Explanation:

The Total amount is given as the sum of the Principal amount and the interest amount;

$Amount= P+IAmount=5000+1500Amount=6500$

Assuming that the interest is compounded,

The amount, $A$, compounded on an interest, $i$, for a period of t years is given as

$A=P*(1+i)^t\\6500=5000*(1+\frac{2.5}{100})^t\\\frac{6500}{5000}=1.025^t\\ 1.3=1.025^t$

Applying natural logs on both sides

$ln 1.3=ln1.025^t$

Applying laws of logarithms we get

$ln1.3=t*ln1.025\\t=\frac{ln1.3}{ln1.025}\\ t=10.625 years$

Therefore, Ramakant should leave his money in the account for 10.625 years (or 10 years and 7.5 months)