Question

Suppose that $2000 is placed in an account that pays 12% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.(a) Find the amount in the account at the end of 1 year.(b) Find the amount in the account at the end of 2 years.

Answer 1

(a) $2,240.00

(b) $2,508.80

Explanation

Compound interest formula

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

where

• A: final amount, in dollars

,

• P: principal, in dollars

,

• r: interest rate, as a decimal

,

• n: number of times interest is applied per year

,

• t: time in years

(a) Substituting into the formula with P = $2000, r = 0.12 (= 12/100), n = 1 (interest is applied once per year), and t = 1 year, we get:

`\begin{gathered} A=2000(1+(0.12)/(1))^(1\cdot1) \\ A=2,000(1.12) \\ A=\text{ \$}2240 \end{gathered}`

(b) Substituting the same values as item a, except t = 2 years, we get:

`\begin{gathered} A=2,000(1+(0.12)/(1))^(1\cdot2) \\ A=2,000(1.12)^2 \\ A=\text{ \$}2508.80 \end{gathered}`