Question

How much would you have to deposit in an account with a 8% interest rate, compounded monthly to have $800 in your account 8 years later?

PLEASE FAST 100 POINTS

Answer 1

$422.73

Explanation:

To calculate how much would you have to deposit in an account with a 8% interest rate, compounded monthly, to have $800 in your account 8 years later, 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:

• A = $800
• r = 8% = 0.08
• n = 12 (monthly)
• t = 8 years

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

`800=P\left(1+(0.08)/(12)\right)^(12 \cdot 8)`

`800=P\left(1+(1)/(150)\right)^(96)`

`800=P\left((151)/(150)\right)^(96)`

`P=(800)/(\left((151)/(150)\right)^(96))`

`P=422.730824...`

`P=\$422.73\;\sf(nearest\;cent)`

Therefore, you would have to deposit $422.73 in an account with a 8% interest rate, compounded monthly, to have $800 in your account 8 years later.

Answer 2

P =$
`\boxed{\tt 422.73}`

Explanation:

we can use the following formula to solve this question:

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

where:

• A is the future value of the investment
• P is the present value of the investment
• r is the interest rate
• n is the number of times per year the interest is compounded
• t is the number of years

In this case, we have:

• P = $800
• r = 8% = 0.08
• n = 12 (monthly compounding)
• t = 8 years

Substituting value in the above-given formula, We get

`\tt 800 = P* (1 + (0.08)/(12))^(12 * 8)`

800 = P* (1.0066667)^{96}

Solving for P

`\tt P= (800)/( (1.0066667)^(96))`

P= 422.73

Therefore, you would need to deposit $422.73 in an account with an 8% interest rate, compounded monthly to have $800 in your account 8 years later.