QUESTION 03 bookmark_border Select the correct answer Pravin borrowed a sum of money and returned it in three equal quarterly instalments of Rs. 17576 each. Find the sum borrowed, if the rate of interest charged was 16% per annum compounded quarterly. radio_button_unchecked 46900 radio_button_unchecked 48775 radio_button_unchecked 68320 radio_button_unchecked None give direct answer
Question
QUESTION 03 bookmark_border Select the correct answer Pravin borrowed a sum of money and returned it in three equal quarterly instalments of Rs. 17576 each. Find the sum borrowed, if the rate of interest charged was 16% per annum compounded quarterly.
radio_button_unchecked 46900
radio_button_unchecked 48775
radio_button_unchecked 68320
radio_button_unchecked None give direct answer
Solution
To solve this problem, we need to understand that the sum borrowed is the present value of the three future payments of Rs. 17576 each. Since the interest is compounded quarterly, we can use the formula for the present value of an ordinary annuity:
P = PMT * [(1 - (1 + r/n) ^ -nt) / (r/n)]
where: PMT = periodic payment = Rs. 17576 r = annual interest rate = 16% = 0.16 n = number of compounding periods per year = 4 (quarterly) t = number of years = 3/4 (since there are three quarterly payments)
Substituting these values into the formula, we get:
P = 17576 * [(1 - (1 + 0.16/4) ^ -(4*(3/4))) / (0.16/4)]
Solving this equation will give us the sum borrowed.
Please note that this is a complex calculation and you may need a scientific calculator or software to solve it.
The correct answer should be one of the options provided.
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