Question

James wants to be able to make a $30,000 down payment on a new home in three years. If he can invest his savings in an account that earns 6%

interest per year, compounded monthly, about how much will James need to deposit today to achieve his goal?
A.
$25,002
O
B. $25.069
C. $25,189
OD. $35,730

Answer 1

B. $25,069

Explanation:

An interest of 6% per year, compounded monthly it means that he earns 6/12% = 0.5% of what he has invested every month.

If he invests x money what he will have the first month will be :

Money = x*(1+0.005)

The next month:

Money' = Money*(1+0.005) = x *(1+0.005)(1+0.005) = x* (1+0.005)^2

Therefore in this type of interest the formula is:

Money = x*(1+r)^n

Where:

x is the money invested the first time

r is the interest

n is the number of periods

For this problem:

x = what you have to find

r = 0.005

n = 3 years (1 period is 1 month) then the period is 36 months

Money = 30000

Replacing:

30000 = x * (1+0.005)^36

x = 25,069