Question

Wahida borrowed Rs.\[25000\] for \[1\]year \[5\]months at \[12\% \] per annum compounded yearly. Find the amount Wahida paid to settle the account.

Answer 1

Hint: Here we will use a compound interest formula. Also, formulas used to calculate the amount will be used. Time given in months will be converted to year in order to do simplification.

Complete step by step solution:
Compound interest: Compound interest is basically the addition of interest in the loan amount. Its formula is \[\dfrac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}}\] where P stands for Principal, R stands for rate and T stands for time (in years/months).
Amount Formula: \[{\text{A}} = {\text{P}}{\left( {1 + \dfrac{{\text{R}}}{{100}}} \right)^{\text{n}}}\] .
Now, we are given that Wahida borrowed Rs. \[25000\] for \[1\] year\[5\] months at an interest rate of \[12\% \]. After one year interest will be added to the loan amount.
The total amount after one year will be,
${\text{A}} = 25000\left( {1 + \dfrac{{12}}{{100}}} \right) \\
= 25000 \times \dfrac{{112}}{{100}} \\
= 28000 $
Now, we will calculate the interest of \[5\] months, we can write \[5\] months as \[\dfrac{5}{{12}}\] years also.
Calculation of interest is given as,
$ = 28000 \times \dfrac{5}{{12}} \times \dfrac{{12}}{{100}} \\
= 1400 $
The total amount that Wahida paid to settle the account is equal to the sum of the amount after one year with the interest of five months. Sum is given as, \[28000 + 1400 = 29400\].

Hence, the total amount that has to be paid by Wahida to settle her account is Rs.\[29400\].

Note: In such types of problems direct formulas of compound interest, simple interest and amounts are used. So, it is important to remember these formulas as without them such problems cannot be solved. Also, if the given time is of the type \[1\] year\[5\] months then the amount for \[1\] year and for \[5\] months should be calculated separately.