Question

Solve a man borrows rs. 2100 and undertakes to pay back with compound interest @ 10% p.A. In 2 equal yearly installments at the end of first and second year. What is the amount of each installment?

Answer 1

Answer:

The amount of each installment is 2100.

Step-by-step explanation:

A compound interest is defined as the addition of the interest to sum of a loan or the deposit.

• Types of compound interest:

1) Monthly compound Interest

2) Daily compound interest

3) Annual compound Interest

Given that:

Man borrows amount of = 2100

Compound interest = 10% p.a.

Yearly installment = 2 equal

To find:

The amount of each installment=?

Solution:

Let us consider, the installment to be x.

Now, we are going to take,

the value of first installment before 1 year =   $x/(1+10/100)$ = $10x/11$

Again, let us take the value of,

the second installment before 2 year = $x/(1+10/100)^{2}$  = $100x/121$

We know that,

When the value given above will be equal to the principal.

$10x/ 11 +100x/121$ = $2100$

$110x+100x/ 121$ = $2100$

$210x/121$ =$2100$

Finally, the value of x,

x = $2100$

Therefore, the amount of each installment is 2100.

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Answer 2

The amount of each installment is Rs.1210.

Step-by-step explanation:

Given:

A man borrows rs. 2100.

Compound interest @ 10% p.A. In 2 equal yearly installments at the end of first and second year.

To Find:

The amount of each installment.

Formula Used:

$X=Y(1+\frac{Z}{100} )^{T}$                            ---------------------formula no.01.

X= represents the new principal sum or the total amount of money after compounding period

Y= represents the original amount or initial amount

Z= is the annual interest rate(in percentage)

T= represents the number of years

Solution:

As given, a man borrows rs. 2100.

Y= Rs.2100

Let the the amount of each installment k.

As given,Compound interest @ 10% p.A. In 2 equal yearly installments at the end of first and second year.

The value of the principal after 2 years = The value of 1st installment after 1 year + the value of 2nd installment

$2100(1+\frac{10}{100} )^{2}=k(1+\frac{10}{100} ) +k$

$2100(\frac{110}{100} )^{2}=k(\frac{110}{100} ) +k$

$2100(\frac{121}{100} )=k(\frac{11}{10} ) +k$

$2100(\frac{121}{100} )=(\frac{21}{10} ) k$

$k=\frac{2100\times 121\times10}{21\times 100}$

$k= Rs.1210$

Thus,the amount of each installment is Rs.1210.

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