# Aptitude - Compound Interest

### MCQ

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Q 11.

Find the effective annual rate of interest corresponding to a nominal rate of 6% p.a. compounded half-yearly.

Options:

• 6.03%

• 6.05%

• 0.07%

• 6.09%

Let Principal P = 100, Rate = R, n = 1

When compounded half-yearly,

A = P (1 + (R/2)/100)2n
= 100 (1 + 3/100)2
= 106.09

Effective Rate = (A - P)%
= 6.09%

Q 12.

Find the rate of interest per annum if a sum of money invested at compound interest amount to \$800 and \$840 in 3 and 4 years respectively.

Options:

• 5%

• 6%

• 7.25%

• 8%

SI on \$800 for 1 year = 840 - 800 = \$40

Rate = (100 x SI) / (P x T)
= (100 x 40) / (800 x 1)

Q 13.

If a sum of money invested at compound interest doubles itself in 5 years then, in how many years will it become 8 times at the same rate of interest?

Options:

• 11 years

• 13 years

• 15 years

• 17 years

1st part:

P(1 + R/100)5 = 2P

or, (1 + R/100)5 = 2     ... (i)

2nd part:

P(1 + R/100)n = 8P

or, (1 + R/100)n = 8
or, (1 + R/100)n = 23
or, (1 + R/100)n = {(1 + R/100)5}3     ... using (i)

Q 14.

Find the least number of complete years in which a sum of money put out at 20% compound interest will be more than double.

Options:

• 3 years

• 4 years

• 5 years

• 6 years

P(1 + 20/100)n > 2P

Q 15.

Monty borrowed a sum of money from a bank and paid it back in two annual installments of Rs. 882 each allowing 5% compound interest. What was the sum borrowed?

Options:

• 1640

• 1650

• 1660

• 1670

Present worth of Rs. 882 due 1 year hence
= P/(1 + R/100)
= 882/(1 + 5/100) ... (i)

Present worth of Rs. 882 due 2 years hence
= P/(1 + R/100)2
= 882/(1 + 5/100)2 ... (ii)

Sum borrowed
= (i) + (ii)
= 1640

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