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

B. $25,069

Step-by-step 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