Question

Vince puts 400.00 into an account to use for school expenses the account earns 15% interest compounded monthly how much will be in the account after 6 years?

Answer 1

Given in the question:

a.) Vince puts 400.00 into an account.

b.) The account earns 15% interest compounded monthly.

c.) How much will be in the account after 6 years?

For this type of interest problem, since been mentioned that this is a compounded interest, we will be using the compounded interest formula:

`A\text{ = }P(1\text{ + }(r)/(n))^(nt)`

Where,

A = Amount after a certain amount of time.

P = Principal/Initial Amount = 400

r = Interest Rate (In Decimal Form) = 15%/100% = 0.15

n = Number of times interest is compounded = Monthly = 12

t = Time (In Years) = 6 years

Let's plug in the values in the formula to be able to get the value of A.

`A\text{ = }P(1\text{ + }(r)/(n))^(nt)`
`A\text{ = }(400)(1\text{ + }(0.15)/(12))^((12)(6))`
`A\text{ = }(400)(1\text{ + }0.0125)^((72))`
`A\text{ = }(400)(1.0125)^((72))`
`A\text{ = }978.3681\text{ }\approx\text{ 978.37}`

Therefore, Vince's account will be 978.37 after 6 years.