Question

Luther opened a savings account and deposited $400.00. The account earns 4% interest,compounded annually. If he wants to use the money to buy a new bicycle in 2 years, howmuch will he be able to spend on the bike?nt= P(1+7)1Use the formula A = P (1 + r/n)where A is the balance (final amount), P is the principal(starting amount), r is the interest rate expressed as a decimal, n is the number of times peryear that the interest is compounded, and t is the time in years.Round your answer to the nearest cent.

Answer 1

To solve this problem, we must use the formula:

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

Where:

• A = final amount = ?,

,

• P = starting amount = $400.00,

,

• r = interest rate in decimals = 4% = 0.04,

,

• n = number of times per year that the interest is compounded = 1 (because interest is compounded annually),

,

• t = time in years = 2.

Replacing the data of the problem in the equation above, we get:

`A=400.00\cdot(1+0.04)^2=432.64.`

Answer

After 2 years, he will be able to spend $432.64 on the bike.