Question

Dr. Farooq buys an annuity that makes regular payments each accounting Rs 12,000 per year for 15 years. He is to receive level payments at beginning of every year. What premium should Maxwell be willing to pay for this annuity assuming that effective interest rate is 13.5%

Answer 1

To calculate the present value of an annuity with payments made at the beginning of each period, you can use the present value of an annuity due formula. The formula is:

\[ PV_{\text{due}} = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \times (1 + r) \]

where:

- \( PV_{\text{due}} \) is the present value with payments at the beginning,

- \( P \) is the periodic payment,

- \( r \) is the interest rate per period, and

- \( n \) is the total number of periods.

In this case, \( P = Rs 12,000 \), \( r = 0.135 \) (13.5% expressed as a decimal), and \( n = 15 \). Substitute these values into the formula:

\[ PV_{\text{due}} = Rs 12,000 \times \left( \frac{1 - (1 + 0.135)^{-15}}{0.135} \right) \times (1 + 0.135) \]

Now, calculate each part of the expression:

\[ PV_{\text{due}} = Rs 12,000 \times \left( \frac{1 - (1.135)^{-15}}{0.135} \right) \times (1.135) \]

\[ PV_{\text{due}} \approx Rs 85,590.79 \]

Therefore, Dr. Farooq should be willing to pay approximately Rs 85,590.79 for this annuity with payments made at the beginning of each year.

Answer 2

Dr. Farooq should be willing to pay approximately Rs 74,432.64 for the annuity.

To solve this problem

We can use the present value formula for an ordinary annuity:

Present Value (PV) =
`Payment / (1 + Interest Rate)^N^u^m^b^e^r ^o^f P^e^r^i^o^d^s`

In this case:

• Payment: Rs 12,000 per year
• Interest Rate: 13.5% per year (effective)
• Number of Periods: 15 years

How to Determine Present Value:

First, convert the interest rate from decimal to a percentage:

13.5% * 100% = 13.50%

Plug the values into the formula:

`PV = Rs 12,000 / (1 + 0.1350)^1^5`

Now, let calculate the present value using a calculator: PV ≈ Rs 74,432.64

So, Dr. Farooq should be willing to pay approximately Rs 74,432.64 for the annuity.