Question

Arif took a loan of 80,000 from a bank. If the rate of interest is 10% per annum
1/
find the difference in amounts he would be paying after 3 years if the interest is
(1) compounded annually.
(2) compounded half yearly.
​

Answer 1

Given:-

• Principal = Rs.80000
• Rate = 10% p.a.
• Time = 3 years

To Find:-

• The difference in amounts Atif would be paying after 3 years if the interest is
• (1) Compounded annually
• (2) Compounded half - yearly

Solution:-

(1) Compounded annually

→ We know,

• A = P(1 + r/100)ⁿ

Therefore,

A = 80000(1 + 10/100)³

= A = 80000(1 + 1/10)³

= A = 80000[(10 + 1)/10]³

= A = 80000 × (11/10) × (11/10) × (11/10)

= A = 80 × 11 × 11 × 11

= A = 106480

∴ Amount after 3 years if the interest is compounded annually is Rs.106480.

________________________________

(2) Compounded half-yearly

→ We know,

• A = P(1 + r/200)²ⁿ

Therefore,

A = 80000(1 + 10/100)²*³

= A = 80000(1 + 1/10)⁶

= A = 80000[(10 + 1)/10)]⁶

= A = 80000(11/10)⁶

= A = 80000 × 11/10 × 11/10 × 11/10 × 11/10 × 11/10 × 11/10

= A = 141724.88

∴ Amount after 3 years if the interest is compounded annually will be Rs.141724.88

________________________________

Difference in amounts,

= 141724.88 - 106480

= Rs.35244.88

∴ Difference in amounts Atif would be paying after 3 years will be Rs.35244.88.

________________________________

Answer 2

Given:-

• Principal = Rs.80000
• Rate = 10% p.a.
• Time = 3 years

To Find:-

• The difference in amounts Atif would be paying after 3 years if the interest is
• (1) Compounded annually
• (2) Compounded half - yearly

Solution:-

(1) Compounded annually

→ We know,

• A = P(1 + r/100)ⁿ

Therefore,

A = 80000(1 + 10/100)³

= A = 80000(1 + 1/10)³

= A = 80000[(10 + 1)/10]³

= A = 80000 × (11/10) × (11/10) × (11/10)

= A = 80 × 11 × 11 × 11

= A = 106480

∴ Amount after 3 years if the interest is compounded annually is Rs.106480.

________________________________

(2) Compounded half-yearly

→ We know,

• A = P(1 + r/200)²ⁿ

Therefore,

A = 80000(1 + 10/100)²*³

= A = 80000(1 + 1/10)⁶

= A = 80000[(10 + 1)/10)]⁶

= A = 80000(11/10)⁶

= A = 80000 × 11/10 × 11/10 × 11/10 × 11/10 × 11/10 × 11/10

= A = 141724.88

∴ Amount after 3 years if the interest is compounded annually will be Rs.141724.88

________________________________

Difference in amounts,

= 141724.88 - 106480

= Rs.35244.88

∴ Difference in amounts Atif would be paying after 3 years will be Rs.35244.88.

________________________________