Question

'Dr. Singh and Mr. Jones plan to donate money to the local ice hockey team. Dr. Singh will give $500 at the end of each year for 9 years. Mr. Jones would rather give a single donation now. What amount can he denote today that will equal the value of Dr. Singh's annual gifts if the fund earns 7.5% annually?

Answer 1

Mr. Jones should donate a single payment of approximately $3,256.71 today to have the same value as Dr. Singh's annuitized donations over 9 years, given a 7.5% annual interest rate.

Step-by-step explanation:

The question involves determining the present value of an annuity. Dr. Singh is donating money as an annuity, which is a series of equal payments made at regular intervals.

Using the present value of an annuity formula, we can calculate the equivalent amount Mr. Jones should donate today, assuming a 7.5% annual interest rate.

Present Value of Annuity formula:

PVA = PMT [1 - (1 + r)^-n] / r

Where:

• PVA is the present value of the annuity
• PMT is the annual payment (in this case, $500)
• r is the annual interest rate (7.5% or 0.075)
• n is the number of periods (9 years)

Plugging in the values we have

PVA = 500 [1 - (1 + 0.075)^-9] / 0.075.

Calculating this we find out that Mr. Jones should donate a single payment of approximately $3,256.71 today to equal Dr. Singh's total contributions over 9 years.