Jeanette needs $15,000 as a down payment for a house six years from now. She earns 3.5% on her savings. Jeanette can either deposit one lump sum today for this purpose or she can wait a year and deposit a lump sum. How much additional money must Jeanette deposit if she waits for one year rather than making the deposit today?
A) $121.03
B) $166.67
C) $307.00
D) $333.33
E) $427.09

Question

Quizplus · Accepted Answer

To find out how much additional money Jeanette must deposit if she waits for a year, we first calculate the present value of $15,000 needed in six years at an interest rate of 3.5%. The formula for present value (PV) is $PV = \frac{FV}{(1 + r)^n}$, where FV is the future value, r is the annual interest rate, and n is the number of years.For depositing today (n = 6 years):$$PV = \frac{15,000}{(1 + 0.035)^6} = \frac{15,000}{1.226} ≈ 12,234.97$$If she waits a year, she will only have 5 years for the investment to grow, so (n = 5 years):$$PV = \frac{15,000}{(1 + 0.035)^5} = \frac{15,000}{1.187} ≈ 12,662.06$$The difference between the two amounts is how much additional money she must deposit if she waits for a year:$$12,662.06 - 12,234.97 = 427.09$$Therefore, Jeanette must deposit an additional $427.09 if she waits for a year to make the deposit.

Jeanette Needs $15,000 as a Down Payment for a House