Question

Prathibha borrows 47000 from a finance company to buy her first car. The rate of
simple interest is 17% and she borrows the money over a 5 year period. Find: (a) How
much amount Prathibha should repay the finance company at the end of five years. (b) her
equal monthly repayments.
​

Answer 1

➤ Given :-

Principle :- ₹47000

Rate of interest :- 17%

Time :- 5 years

$\:$

➤ To Find :-

• Total amount to be paid back.
• Equal monthly repayments.

$\:$

➤ Formula required :-

Total amount :-

${\tt \large \dashrightarrow{\orange{\boxed{\tt \gray{Simple \: Interest + Principle}}}}}$

Equal monthly repayments :-

${\tt \large \dashrightarrow{\orange{\boxed{\tt \gray{\dfrac{Total \: Amount}{Time \: taken \: (months)}}}}}}$

$\:$

★ How to do :-

Here, we are given with the principle amount, rate of interest and time taken to return the money back. We should find the total amount she returns back after the period and her equal monthly payment expenses. To find the total amount, first we should find the simple interest by multiplying the principle, rate, time and then divide by 100. Then, we can use the first formula given above. To find her monthly repayments, we can divide the total amount and the time taken in months format. So, let's solve!!

$\:$

➤ Solution :-

Simple Interest :-

${\tt \leadsto \dfrac{47000 \times 17 \times 5}{100}}$

${\tt \leadsto \dfrac{\cancel{47000} \times 17 \times 5}{\cancel{100}} = \dfrac{470 \times 17 \times 5}{1}}$

${\tt \leadsto 470 \times 85 = 39950}$

Now,

Total Amount :-

${\tt \leadsto 39950 + 47000}$

${\tt \leadsto \boxed{\tt Rs \: \: 86950}}$

$\:$

Equal monthly repayments :-

${\tt \leadsto \dfrac{86950}{(5 \times 12)}}$

${\tt \leadsto \dfrac{86950}{60}}$

${\tt \leadsto \cancel \dfrac{86950}{60} = \boxed{\tt Rs \: \: 1449.16}}$

$\Huge\therefore$ The total amount to be returned back is ₹86950 and the monthly repayments is ₹1449.16.

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$\dashrightarrow$ Some related formulas :-

${\longrightarrow \boxed{\sf Simple \: Interest = \dfrac{P \times R \times T}{100}}}$

${\longrightarrow \boxed{\sf Principle = \dfrac{SI \times 100}{R \times T}}}$

${\longrightarrow \boxed{\sf Rate \: of \: Interest = \dfrac{SI \times 100}{P \times T}}}$

${\longrightarrow \boxed{\sf Time = \dfrac{SI \times 100}{P \times T}}}$