Question

A sum of Rs. 8000 is borrowed at 5%, compounded annually, and paid back in 3 equal annual installments. What is the amount of each installment?
Options

Rs. 2937.67

Rs. 3000

Rs. 2037.67

Rs. 2739.76

Answer 1

Step-by-step explanation:

P - 8000

R -5%

$a = p(1 + \frac{r}{100} )n$

$a = 8000(1 + \frac{5}{100} )$

$a = 8000 \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20}$

gv

Answer 2

The amount of each installment=Rs 2937.67

Step-by-step explanation:

Principle amount=P=Rs 8000

Rate of interest=5%

Total number of installment,n=3

Let x be the amount of each installment

The general formula for installment in compound interest

$P=\frac{x}{1+\frac{r}{100}}+\frac{x}{(1+\frac{r}{100})^2}+...+\frac{x}{(1+\frac{r}{100})^n}$

Where P=Principle amount

x=Amount of each installment

r=Rate of interest

n=Number of installment

Substitute the values then we get

$8000=\frac{x}{1+\frac{5}{100}}+\frac{x}{(1+\frac{5}{100})^2}+\frac{x}{(1+\frac{5}{100})^3}$

$8000=\frac{20x}{21}+x(\frac{20}{21})^2+x(\frac{20}{21})^3$

$8000=\frac{20x}{21}(1+\frac{20}{21}+\frac{400}{441})$

$880=\frac{20x}{21}\times \frac{1261}{441}$

$x=\frac{8000\times 21\times 441}{20\cdot 1261}$

x=2937.67

Hence, the amount of each installment=Rs 2937.67

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