Question

$1,200 are deposited into an account with a 6.75% interest rate, compounded quarterly.

Find the accumulated amount after 20 years. Round your answer to the nearest cent (hundredth).

Answer 1

$4,577.06

Explanation:

To find the account balance after 20 years of $1,200 deposited into an account with an interest rate of 6.75% compounded quarterly, we can use the compound interest formula.

`\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+(r)/(n)\right)^(nt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}`

Given values:

• P = $1,200
• r = 6.75% = 0.0675
• n = 4 (quarterly)
• t = 20 years

Substitute the given values into the formula and solve for A:

`A=1200\left(1+(0.0675)/(4)\right)^(4* 20)`

`A=1200\left(1+0.016875\right)^(80)`

`A=1200\left(1.016875\right)^(80)`

`A=1200\left(3.814218976...\right)`

`A=4577.0627713...`

`A=4577.06\; \sf (nearest\;hundredth)`

Therefore, the account balance after 20 years is $4,577.06 (rounded to the nearest cent).

Answer 2

$4,577.06

Explanation:

Use the interest equation:

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

where A is the final amount,

P is the initial amount,

r is the annual interest rate (as a decimal),

n is the number of compounding per year,

and t is the number of years.

In this case:

P = 1200

r = 0.0675

n = 4

t = 20

Plug in and find A:

A = 1200 (1 + (0.0675 / 4))^(4 × 20)

A = 1200 (1 + 0.016875)^80

A = 4577.06