Question

Calculate the amount that needs to be repaid at the end of 3 years if a sum of 20, 000 is borrowed on simple interest for the first year and on compound interest for the next 2 years, with the rate of interest in both the cases being 8% p.a.

Answer 1

Given:

A sum of 20000 is borrowed on simple interest for the 1st year and on compound interest for the next 2 years with the rate of interest being 8% for both cases.

To Find:

Amounts that needs to be repaid after 3 years.

Solution:

As the interest is being calculated in different ways let's consider both ways,

• 1st year

For the 1st year, we need to calculate interest using simple interest

                                        $I=\frac{P*R*T}{100}$

now putting all the values i.e.

$P$=20000

$R$=8%

$T$= 1 year

                                           $I=\frac{20000*8*1}{100} \\ =1600$

So, for the 1st year interest is 1600.

• 2nd and 3rd year

For these years we need to calculate interest using compound interest

                                        $A=P(1+r)^{n}$

now putting the values

$P$=21600

$r$=8%

$n$=2

                                        $A=20000(1+0.08)^{2}$

                                            $=20000*1.1664\\=23328$

So, after 3 years the total amount to be repaid will be

                                     $A=20000+1600+23328\\ =44928$

Hence, the total amount to be repaid after 3 years is 44928.