Applied Mathematics

Financial Mathematics

Medium

applied

At what rate converted semi-annually will the present value of perpetuity of ₹750/- payable at the end of each 6 months be ₹ 25000?(where p.a. denotes per annum)

0.6%p.a.

0.06% p.a.

6% p.a.

0.006% p.a.

✅ Correct Option: 3

For a perpetuity, present value $=\frac{R}{i}$ , so $25000=\frac{750}{i}$ and $i=0.03$ per half-year.

That is $3\%$ per half-year, i.e. a nominal rate of $6\%$ per annum compounded semi-annually.

2023: 23 May Shift 3

The effective rate that is equivalent to a nominal rate of 16% compounded semi-annually is :

2023: 11 Aug Shift 1

At 8% converted quarterly the present value of perpetuity of Rs. 8000 payable at the end of each quarter ( in rupees) is :

2026: 29 May Shift 2

A person invested ₹y in a mutual fund and the value of the investment at the time of redemption was ₹x. If he invested the amount for 3 years and the compound annual growth rate of his investment is 10 %, then the value of $\frac{y}{x}$ is:

2023: 23 May Shift 3

Mr. X invested Rs.20,000 in year 2022 for 5 years. If Compound annual growth rate for that investment turned out to be 12%, the end value of the investment will be : {Use $(1.12)^5 = 1.76$ }

2022: 25 May Shift 1

A person takes a car loan of Rs 9,00,000 at the rate of 12% per annum for 5 years from a bank. The EMI under flat rate system is:

2026: 29 May Shift 2

Which of the following is true about the sinking fund ?

At what rate converted semi-annually will the present value of perpetuity of ₹750/- payable at the end of each 6 months be ₹ 25000?(where p.a. denotes per annum)

Solution

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