How much must be invested now to receive €20,000 for 15 years if the first €20,000 is received today and the rate is 9%?

Question

Quizplus · Accepted Answer

To calculate the present value of an annuity, we need to use the formula:

PV = (A / r) * (1 - (1 + r)^(-n))

Where:
PV = Present Value
A = Annuity Payment
r = Interest rate
n = Number of periods

In this case, the annuity payment is €20,000 per year for 15 years, and the interest rate is 9% per year. Therefore, we can calculate the present value of the annuity as follows:

PV = (€20,000 / 0.09) * (1 - (1 + 0.09)^(-15))
PV = €175,723.12

However, we also received €20,000 today, so we need to subtract that amount from the present value to get the amount that needs to be invested now:

Investment = PV - €20,000
Investment = €175,723.12 - €20,000
Investment = €155,723.12

Therefore, the best choice is (B) €175,723.

How Much Must Be Invested Now to Receive €20,000 for 15