You are planning to purchase a house in 5 years and want to

You are planning to purchase a house in 5 years and want to save for a downpayment. If you deposit $5,000 each year into an account earning 3% interest, how much will have for a mortgage down payment?

Solution

Time period is five years

Deposit per year is $5000

Interest rate per year is 3%

$5000 which is invested right now will earn 3% interest for five years

$5000 which is invested after the first year will earn 3% interest for the remaining four years

$5000 which is invested after the second year will earn 3% interest for the remaining three years

$5000 which is invested after the third year will earn 3% interest for the remaining two years

$5000 which is invested after the forth year will earn 3% interest for the remaining one years

So the total amount after five years would be:

5000(1+0.03)^5 + 5000(1+0.03)^4 + 5000(1+0.03)^3 + 5000(1+0.03)^2 + 5000(1+0.03)

This comes out to be equal to $27342.05