Statistics & Applications

Financial Math

Medium

applied

At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 20000?

10 %

12 %

8 %

11 %

✅ Correct Option: 1

The payment amount is Rs. 1,000 (received every 6 months).

The present value is Rs. 20,000.

For a perpetuity, the relationship between present value, payment, and interest rate per period is:

Present Value $= \dfrac{\text{Payment}}{\text{Interest Rate per period}}$

Rearranging:

Interest Rate per period $= \dfrac{\text{Payment}}{\text{Present Value}}$

Since payments occur every 6 months, the calculation gives the 6-month interest rate:

Interest rate (per 6 months) $= \dfrac{1000}{20000}$

$= \dfrac{1}{20}$

$= 0.05$

$= 5\%$ per 6 months

There are 2 six-month periods in a year.

Annual Rate $= 5\% \times 2$

$= 10\%$ per annum

Therefore, the rate of interest is 10%.

2026: 19 May Shift 1

Mrs. Soma takes a loan of ₹ 5,00,000 with 10% annual interest rate for 5 years. What will be her EMI under flat rate system?

2026: 12 May Shift 2

Rama takes a personal loan for a car worth ₹5,00,000 at an interest rate of 7% per annum to be repaid by equal monthly instalments (EMI) in 5 years. Using flat rate method, EMI will be:-

2024: 16 May Shift 1

Match List-I with List-II:

List-I Property Type	List-II EMI amount (in ₹)
(A) P	(I) 25,600
(B) Q	(II) 38,400
(C) R	(III) 32,000
(D) S	(IV) 35,200

2025: 13 May Shift 2

At 6% converted quarterly, the present value of a perpetuity of ₹ 900 payable at the end of each quarter is:

2025: 13 May Shift 1

A person invested ₹ 20000 in a mutual fund in year 2018. The value of the mutual fund increased to ₹ 32000 in year 2023. The compound annual growth rate of his investment is:

[Given that $(1.6)^{1/5} = 1.098]$

2026: 30 May Shift 2

Shyamaji takes a loan of ₹20,00,000 with 10% annual interest rate for 10 years. What will be her EMI under flat rate system?

At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 20000?

Solution

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