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
View Answer

Answer: d
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
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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
View Answer

Answer: b
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
View Answer

Answer: c
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
View Answer

Answer: a
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%
View Answer

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

Answer: b
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 %
View Answer

Answer: b
Explanation: Since, the interest is compounded quarterly
Rate = 10%
= \(\frac{10}{4}\) = \(\frac{5}{2}\)%
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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
View Answer

Answer: d
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
View Answer

Answer: b
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.
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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
View Answer

Answer: b
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

Sanfoundry Global Education & Learning Series – Mathematics – Class 8.

To practice Mathematics Aptitude Test for Schools, here is complete set of 1000+ Multiple Choice Questions and Answers.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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