Question

How much will 80,000 amount to in $2\dfrac{1}{2}$ years if the interest rate is $8%$ p.a. compounded annually?

Answer 1

Hint: In order to calculate the amount, in the question it is provided the principal, rate of interest, and time which is compounded yearly. To calculate the amount directly, there is a formula i.e.
${\text{A = P}}{\left( {1 + \dfrac{{\text{R}}}{{100}}} \right)^{\text{n}}}$ where A is amount, P is principle, R is rate of interest and n is number of compounds per year.

Complete step by step answer:
Now, From the question,
Principal (p)\[\]
Rate (r)$ = 8\% $ per annum$=\dfrac{8}{2}=4%$ half yearly (Rate converted to half yearly from yearly as required)
Time (t)$=2\dfrac{1}{2}$years$ = \dfrac{5}{2} \times 2 = 5$half years (time converted to half year from year as per the rate)
Then, by using the formula,
$\text{A=P}{{\left( 1+\dfrac{\text{R}}{100} \right)}^{\text{n}}}$
$=80,000{{\left( 1+\dfrac{4}{100} \right)}^{5}}$
$=80,000{{\left( \dfrac{104}{100} \right)}^{5}}$
$= 97332.23$
$\Rightarrow {\text{ CI = Rs }}97332.23 - 80000 = {\text{ Rs 17332}}{\text{.23}}$

$\therefore $Compound interest is 17332.23

Additional Information:
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest. For example, monthly capitalization with interest expressed as an annual rate means that the compounding frequency is 12, with time periods measured in months.

Note:
While solving this question, we should be careful with the values given in the question. It must be noted while solving that the rate of interest is given per annum or annually whereas the time is given as a fraction of years i.e. two and a half years. Therefore, we need to convert the rate half-yearly and the time to the half-year too. This will make the question take much more years to put in the formula and solve it.