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} = 2^{3}

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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