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Suppose Deshaun places
$8000 in an account that pays
2% 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.

$

Suppose Deshaun places $\$ 8000$ in an account that pays $2 \%$ interest compounded each year. Assume that no withdrawals are made from the account. $\newline$ Follow the instructions below. Do not do any rounding. $\newline$ (a) Find the amount in the account at the end of $1$ year. $\newline$ $\square$ $\newline$ (b) Find the amount in the account at the end of $2$ years. $\newline$ $\$$

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Compound interest: word problems

Full solution

Q. Suppose Deshaun places

\$ 8000

in an account that pays

2 \%

interest compounded each year. Assume that no withdrawals are made from the account.

\newline

Follow the instructions below. Do not do any rounding.

\newline

(a) Find the amount in the account at the end of

1

year.

\newline

\square

\newline

(b) Find the amount in the account at the end of

2

years.

\newline

\$

Given Values: $P = \$8000$ , $r = 2\%$ or $0.02$ , $n = 1$ (since interest is compounded annually), $t = 1$ year for part (a).
Calculate Amount After $1$ Year: Use the formula $A = P(1 + r/n)^{(nt)}$ to find the amount after $1$ year.
Amount After $1$ Year: $A = 8000(1 + 0.02/1)^{(1*1)} = 8000(1 + 0.02)^1 = 8000(1.02)^1$ .
Calculate Amount After $2$ Years: $A = 8000 \times 1.02 = 8160$ .
Amount After $2$ Years: For part (b), now calculate the amount after $2$ years with $t = 2$ .
Amount After $2$ Years: For part (b), now calculate the amount after $2$ years with $t = 2$ . $A = 8000(1 + 0.02/1)^{(1*2)} = 8000(1 + 0.02)^2 = 8000(1.02)^2$ .
Amount After $2$ Years: For part (b), now calculate the amount after $2$ years with $t = 2$ . $A = 8000(1 + 0.02/1)^{(1*2)} = 8000(1 + 0.02)^2 = 8000(1.02)^2$ . $A = 8000 \times 1.02^2 = 8000 \times 1.0404$ .
Amount After $2$ Years: For part (b), now calculate the amount after $2$ years with $t = 2$ . $A = 8000(1 + 0.02/1)^{(1*2)} = 8000(1 + 0.02)^2 = 8000(1.02)^2$ . $A = 8000 \times 1.02^2 = 8000 \times 1.0404$ . $A = 8000 \times 1.0404 = 8323.20$ .

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