Question

Mr. Rahul invested ₹2,000 each year at the start of the year, compounded half-yearly at a rate of 10%. After a year and a half, he withdraws ₹1,000. Determine his savings at the start of the third year.

• A. ₹6,636
• B. ₹5,586
• C. ₹6,431
• D. ₹2,800

Answer 1

The correct option is B ₹5,586

Rate of interest r = 10%, compounded half-yearly
At the start of the first year,
Principal, P = ₹2,000
Amount after 6 months = $2,000+2,000\times \frac{10}{2\times 100}$
$=2,000+100=₹2,100$
$\therefore$Principal after 6 months = ₹2,100
Amount after a year = $2,100+2,100\times \frac{10}{2\times 100}$
$=2,100+105=₹2,205$
Amount after a year = ₹2,205
Amount at the start of second year = 2,205 + 2,000 = ₹4,205
(₹2,000 invested at the beginning of every year)
Amount after one and a half year = $4,205+4,205\times \frac{10}{2\times 100}$
$=4,205+210.25=₹4,415.25$
He withdraws ₹1,000 after a year and half.
$\therefore$Principal after one and a half years = 4,415.25 - 1,000 = ₹3,415.25
Amount after two years = $3,415.25+3,415.25\times \frac{10}{2\times 100}$
= 3,415.25 + 170.7625= ₹ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> 3,586.0125
Amount at the beginning of third year = 3,586.0125 + 2,000 = ₹ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> 5,586.0125 = ₹5,586