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Sagot :
Answer:
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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