At what rate of interest per annum will 800 amount to 882 in 1 year when compounded half yearly

Michael borrowed Rs 16000 from a finance company at $10 %$ per annum, compounded half-yearly.

Question:

Michael borrowed Rs 16000 from a finance company at $10 \%$ per annum, compounded half-yearly. What amount of money will discharge his debt after $1 \frac{1}{2}$ years?

Solution:

Principal amount $=$ Rs. 16000

Rate of interest $=10 \%$ per annum $=5 \%$ for half year

Time $=1 \frac{1}{2}$ years $=3$ half years

Principal for the first half year $=$ Rs. 16000

Interest for the first half year $=$ Rs. $\left(\frac{16000 \times 5 \times 1}{100}\right)=$ Rs. 800

Now, amount at the end of the first half year $=$ Rs. $(16000+800)=$ Rs. 16800

Principal for the second half year $=$ Rs. 16800

Interest for the second half year $=$ Rs. $\left(\frac{16800 \times 5 \times 1}{100}\right)=$ Rs. 840

Now, amount at the end of the second half year $=$ Rs. $(16800+840)=$ Rs. 17640

Principal for the third half year $=$ Rs. 17640

Interest for the third half year $=$ Rs. $\left(\frac{17640 \times 5 \times 1}{100}\right)=$ Rs. 882

Now, amount at the end of the third half year $=$ Rs. $(17640+882)=$ Rs. 18522

$\therefore$ The amount of money Michael has to pay the finance company after $1 \frac{1}{2}$ years is Rs $18522 .$

Q 11.

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

Options:

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:

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

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:

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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