Question

A village completed a water tower costing $921,000, with a government grant covering $490,000. To finance the balance in 30 years, they plan to charge homeowners a one-time flat fee. If the investment earns 7.8% interest compounded monthly, how much should the village invest now to cover the future balance? (Round to the nearest cent)

a. $310,000
b. $381,450
c. $275,600
d. $429,800

Answer 1

To cover the future balance of $921,000 over 30 years, the village should invest approximately $275,600 with an interest rate of 7.8% compounded monthly.

Step-by-step explanation:

To finance the balance of $921,000 in 30 years, the village should invest:

Step 1: Calculate the future value of the balance.

Future value = Principal x (1 + interest rate/compounding frequency)^(compounding frequency x time)

Future value = ($921,000 - $490,000) x (1 + 0.078/12)^(12 x 30)

Future value = $431,000

Step 2: Calculate the present value of the future value.

Present value = Future value / (1 + interest rate/compounding frequency)^(compounding frequency x time)

Present value = $431,000 / (1 + 0.078/12)^(12 x 30)

Present value = $275,600 (rounded to the nearest cent)

The village should invest approximately $275,600 to cover the future balance.