Question

You are saving towards purchasing a house and currently have $20,000 in an account that earns 8%, compounded monthly. You would like to be able to purchase a $300,000 house and make a full 20% down payment.

a. How long will it take for your current savings to be enough for the down payment?

b. If you add $10,000 to the account today, how long will it take for your current savings to

be enough for the down payment?

Answer 1

a)

20% down payment = 0.20 x $ 300,000

20% down payment = $ 60,000

The duration it will take for the current savings to be enough for the down payment can be found using the future value of investment equation

Future value = Present value × (1+interest rate)ⁿ

In the above equation we have to solve for the value of t

By taking natural logarithms on both the sides of the equation, the value of t can be solved

t = 13.78 years

Hence it will take 13.78 years for the current savings to be enough for the down payment.

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b)

If $ 10,000 is added to the account today

t = 8.69 years

Hence it will take 8.69 years for the current savings to be enough for the down payment if $ 10,000 is added to the account today.