Suppose your client wishes to purchase an annuity that pays $50,000 each year for 5 years, with the first payment 4 years from now. At an interest rate of 10%, how much would the client need to invest now

The amount the client would need to invest now is $182,143.58.

Explanation:

This can be calculated using the following two steps:

Step 1: Calculate the present value (PV) of the amount invested 4 years from now

This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV4 = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV4 = Present value of the amount invested 4 years from now = ?

P = Annual payment = $50,000

r = Interest rate = 10%, or 0.10

n = number of years the annual payment will be received = 5

Substitute the values into equation (1), we have:

PV4 = $50,000 * ((1 - (1 / (1 + 0.10))^5) / 0.10)

PV4 = $189,539.34

Step 2: Calculate the amount the client would need to invest now

This can be calculated using the present value formula as follows:

PV = PV4 / (1 + r)^n …………………………. (2)

Where:

PV = Present value or the amount the client would need to invest now = ?

PV4 = Present value of the amount invested 4 years from now = $189,539.34

r = Interest rate = 10%, or 0.10

n = number of years of PV4 from now = 4

Substituting the relevant values into equation one, we have:

PV = $189,539.34 / (1 + 0.01)^4

PV = $182,143.58

Therefore, the amount the client would need to invest now is $182,143.58.

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