Applied Mathematics

Financial Mathematics

Medium

applied

If the cash equivalent of a perpetuity of Rs.1200 payable at end of each half year is Rs.96,000, the annual rate of interest compounded half yearly is :

2.5%

4.5%

✅ Correct Option: 2

Cash equivalent of perpetuity: $P = R/i$ where $i$ is the rate per period. So $96000 = 1200/i$ , giving $i = 1/80 = 0.0125 = 1.25\%$ per half year. Annual rate (compounded half yearly) $= 2 \times 1.25\% = 2.5\%$ .

2023: 30 May Shift 3

The present value of a perpetuity of Rs. 6,240 payable at the beginning of each year, if money is worth 10% effective, is :

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The effective rate $r_e$ corresponding to the nominal rate r compounded continuously is

2023: 7 June Shift 1

A vehicle has a scrap value of Rs 7,50,000 after 6 years of its purchase . If the annual depreciation charge is Rs 55,000, then the original cost of the vehicle is :

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

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Mr. B.M. Wadhwa purchased a car costing ₹20 lakh. It has a useful life of 15 years. The depreciation follows the straight line trend. If the annual depreciation is ₹1,20,000, what is the scrap value of the car ?

2026: 29 May Shift 2

Ms Rajni takes a loan of ₹25,00,000 at an interest of 10% per annum for a period of 20 years. Her EMI using a flat rate method is:

If the cash equivalent of a perpetuity of Rs.1200 payable at end of each half year is Rs.96,000, the annual rate of interest compounded half yearly is :

Solution

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