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.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter