The post office offers an interest of 7% p.a. How much interest would one get if one invests ₹ 50,000 for 3 years without compounding? Class 8

The post office offers an interest of 7% p.a. How much interest would one get if one invests ₹ 50,000 for 3 years without compounding? Class 8

Question 1.

The post office offers an interest of 7% p.a. How much interest would one get if one invests ₹ 50,000 for 3 years without compounding? How much more would one get if it was compounded? Class 8

Solution:

Interest without compounding

= ₹ 50000 × [latex]\frac{7}{100}[/latex] × 3 = ₹ 10500.

Interest with compounding

= ₹ 50000 [latex]\left(1+\frac{7}{100}\right)^3[/latex] - ₹ 50000.

= ₹ 50000 [latex]\left(\frac{107}{100}\right)^3[/latex] - ₹ 50000

= ₹ 50000 × [latex]\frac{107 \times 107 \times 107}{100 \times 100 \times 100}[/latex] - ₹ 50000

= ₹ 61252.15 - ₹ 50000 = ₹ 11252.15

So, more interest = ₹ 11252.15 - ₹ 10500 = ₹ 752.15.

Question 2.

Giridhar borrows a loan of ₹ 12,500 at 12% per annum for 3 years without compounding and Raghava borrows the same amount for the same time period at 10% per annum, compounded annually.

Who pays more interest and by how much? Class 8

Solution:

Giridhar’s interest = ₹ 12500 × [latex]\frac{12}{100}[/latex] × 3

= ₹ 4500.

Raghava’s interest = ₹ 12500 [latex]\left(1+\frac{12}{100}\right)^3[/latex]+ - ₹ 12500

= ₹ 12500 × [latex]\left(\frac{112}{100}\right)^3[/latex] - ₹12500

= ₹ [latex]\frac{12500 \times 112 \times 112 \times 112}{100 \times 100 \times 100}[/latex] - ₹ 12500

= ₹ [latex]\frac{112 \times 112 \times 112}{20 \times 4}[/latex] - ₹ 12500

= ₹ 17561.60 - ₹ 12500 = ₹ 5061.60

Therefore, Raghava pays more interest

₹ 5061.60 - ₹ 4500 = ₹ 561.60.