Question

Ramu borrowed Rs$$7,300$$ from a bank on 8th April, 2002 and settled the account on 3rd March, 2003. What amount did he pay if the rate of interest is $$16\mathrm{\%}$$ per annum?

Answer 1

Hint: Here we will find the time period for which the loan exists and then using the given data we will find the simple interest. We have to find the total amount to be paid for that we will add the principal and simple interest we have found.

Formula used: Let us consider, $$P$$ be the principal, $$T$$ be the time and $$R\mathrm{\%}$$ be the rate of interest, then the simple interest is $$={\displaystyle \frac{PRT}{100}}$$
Then, the amount is $$=P+{\displaystyle \frac{PRT}{100}}$$

Complete step-by-step answer:
It is given that Ramu borrowed Rs. $$7,300$$ from a bank on 8th April, 2002 and settled the account on 3rd March, 2003. The rate of interest is $$16\mathrm{\%}$$ per annum.
We have to find the amount he paid.
At first, we found the time.
Number of days from 8th April, 2002 to 3rd March, 2003 is $$330$$ days.
Now we convert $$330$$ days into years.
$$330$$ days$$={\displaystyle \frac{330}{365}}$$ year
Let us consider, $$P$$ be the principal, $$T$$ be the time and $$R\mathrm{\%}$$ be the rate of interest, then the simple interest is $$={\displaystyle \frac{PRT}{100}}$$
Then, the amount is $$=P+{\displaystyle \frac{PRT}{100}}$$
Let us substitute the values $$P=7300,R=16\mathrm{\%},T={\displaystyle \frac{330}{365}}$$ we get,
The amount is, $$A=7300+{\displaystyle \frac{7300\times {\displaystyle \frac{330}{365}}\times 16}{100}}$$
Let us simplify the amount to be paid we get,
The amount is, $$A=7300+{\displaystyle \frac{105600}{100}}$$
On further simplification we get,
The amount as, $$A=7300+1056$$
We will get the final amount by adding the terms in the right hand side of the equation, we get,
The amount is, $$A=Rs.8356$$
Hence, Ramu has paid Rs. $$8356$$ to the bank.

Additional Information: Simple interest is interest calculated on the principal portion of a loan or the original contribution to a savings account. Simple interest does not compound, meaning that an account holder will only gain interest on the principal, and a borrower will never have to pay interest on interest already accrued.

Note: While converting days into years we should divide the total number of days by number of days in a year. Likewise while converting years into days we have to multiply the year with the number of days in a year.