# Mathematics Questions and Answers – Rate Compounded Annually or Half Yearly

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This set of Mathematics Aptitude Test for Schools focuses on “Rate Compounded Annually or Half Yearly”.

1. What will be the amount to be paid at the end of 7 years on Rs. 3500 at 2% per annum compounded annually?
a) 4428.5
b) 3456.89
c) 4229.56
d) 4020.39

Explanation: Principal = Rs. 3500
Rate = 2%
Time = 7 years
Amount = P (1 + $$\frac{R}{100}$$)t = 3500 (1 + $$\frac{2}{100}$$)7 = 3500 ($$\frac{102}{100}$$)7 = 3500 × 1.148 = 4020.39

2. What will be the amount to be paid at the end of 3 year on Rs. 500 at 10% per annum compounded half-yearly?
a) 657.12
b) 638.14
c) 638.15
d) 645.78

Explanation: Interest is compounded half-yearly
Principal = Rs 500
Rate = 10%
Time = 3 year
Since, interest is charged half-yearly,
Rate = 9 %
= $$\frac{10}{2}$$% = 5%
Time = 3 year = 2 × 3 = 6 half-years
Amount = Principal (1 + $$\frac{R}{100}$$)t
= 500 (1 +$$\frac{5}{100}$$)6
= 500 ($$\frac{21}{20}$$)5
= 638.14

3. A man took loan of Rs. 65,250 from HSBC Bank. If the rate of interest is 9% p.a., then what will be the difference in the amounts he would be paying after 1 year if the interest is compounded quarterly and compounded annually?
a) 72.4
b) 70
c) 69.05
d) 65.5

Explanation: Case 1: Interest is compounded half-yearly
Principal = Rs 65250
Rate = 9%
Time = 1 year
Since, interest is charged half-yearly,
Rate = 9 %
= $$\frac{9}{2}$$%
Time = 1 year = 2 × 1 = 2 half-years
Amount = Principal (1 + $$\frac{R}{100}$$)t
= 65250 (1 + $$\frac{4.5}{100}$$)2
= 65250 ($$\frac{209}{200}$$)2
= 71254.63
Case 2: Interest is compounded quarterly
Principal = Rs 65250
Rate = 9%
Time = 1 year
Since, interest is charged quarterly,
Rate = 9 %
= $$\frac{9}{4}$$%
Time = 1 year = 4 × 1 = 4 quaters
Amount = Principal (1 + $$\frac{R}{100}$$)t
= 65250 (1 + $$\frac{2.25}{100}$$)4
= 65250 ($$\frac{409}{400}$$)4
= 71323.68
Difference in the amounts in both cases = 71323.68 – 71254.63 = 69.05
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4. What will be the time period for a sum taken for 3 years at 12% p.a. compounded half-yearly?
a) 6
b) 3
c) 3.5
d) 4

Explanation: The interest is charged half-yearly
So, the time will be multiplied by 2
Time = 3
= 2 × 3 = 6 half – yearly
The interest will be charged 6 times in 3 years.

5. What will be the rate for a sum taken for 5 years at 8% p.a. compounded half-yearly?
a) 8%
b) 5%
c) 4%
d) 7%

Explanation: The interest is charged half-yearly
So, the rate will be divided by 2
Rate = 8%
= $$\frac{8}{2}$$ = 4%

6. What will be the time period for a sum taken for 4 years 4 months at 10% p.a. compounded quarterly?
a) $$\frac{13}{3}$$
b) 18
c) 4 years 4 months
d) 1 year

Explanation: The interest is charged quarterly,
So, time is multiplied by 4
Time = 4 years 4 months = 4 $$\frac{1}{3}$$ years
= 4 × 4 $$\frac{1}{3}$$ = 4 × $$\frac{13}{3}$$ = $$\frac{52}{3}$$ or 18 quaters approx

7. What will be the rate for a sum taken for 1 ½ years at 10% p.a. compounded quarterly?
a) 2
b) $$\frac{5}{2}$$%
c) 1 ½ %
d) 2 ¼ %

Explanation: Since, the interest is compounded quarterly
Rate = 10%
= $$\frac{10}{4}$$ = $$\frac{5}{2}$$%

8. A sum is taken for 2 years at 12% per annum. If the interest is compounded every 6 months, how many times will the interest be charged in 1 year?
a) 1
b) 3
c) 2
d) 4

Explanation: The interest is charged every six months,
Rate = 12 %
= $$\frac{12}{2}$$ = 6%
Time = 2 years
= 2 × 2 = 4 half – periods
The interest will be charged four times in two years.

9. A sum is taken for 1 ½ years at 10% per annum. If the interest is compounded every 3 months, how many times will the interest be charged in 1 year?
a) 1 ½ years
b) 6
c) 5
d) 4

Explanation: The interest is compounded after every 3 months,
Rate = 10 %
= $$\frac{10}{4}$$ = $$\frac{5}{2}$$%
Time = 1 ½ years or $$\frac{3}{2}$$ years
= 4 × $$\frac{3}{2}$$ = 6 quaters
The interest will be charged six times in one and a half year.

10. What will be the amount to be paid at the end of 18 months on Rs. 12000 at 4% per annum compounded quarterly?
a) 12000
b) 12738.24
c) 13567
d) 13789

Explanation: Principal: Rs. 12000
Rate: 4%
Time: 18 months or 1 ½ year
As the rate is compounded quarterly,
Rate = $$\frac{4}{4}$$ = 1 %
Time = 4 × 1 $$\frac{1}{2}$$ = 6 quaters or 6 quater – years
Amount = Principal (1 + $$\frac{R}{100}$$)t
= 12000 (1 + $$\frac{1}{100}$$)6
= 12000 ($$\frac{101}{100}$$)6
= 12738.24

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