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

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

View Answer

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

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

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

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

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

View Answer

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

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

View Answer

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

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

View Answer

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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