Question

Larry has decided to pursue the American dream and buy his first home. The home he wants is $150,000. The bank will finance 80% of the home, but Larry will need to come up with the remaining 20% as a down payment. The bank loan will be for 30 years, and require monthly payments, and have an interest rate of 6%. Larry currently has $3,000 in his bank account which earns 4% interest annually. Larry will put aside $500 per month into his bank account. How long until Larry can have the down payment of the house?

A. 60.9 months
B. 48.8 months
C. 38.2 months
D. 25.7 months
E. None of the other

Answer 1

Larry will be able to save the down payment for the house in approximately 38.2 months.

Step-by-step explanation:

To calculate how long it will take for Larry to save the down payment, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where A is the future value, P is the principal (initial amount), r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the number of years.

Given that Larry currently has $3,000 and plans to save $500 per month, we can calculate the future value of his savings at the end of each month using compound interest.

Plugging in the values:

A = 3000(1 + 0.04/12)^(12t)

150000 = 3000(1 + 0.04/12)^(12t)

(1 + 0.04/12)^(12t) = 50

Using logarithms, we can solve for t:

12t = log(50)/log(1 + 0.04/12)

t ≈ 38.2 months

Therefore, Larry will be able to save the down payment for the house in approximately 38.2 months.