Question

9. Mildred Hayes wishes to have $80,000 in an account in 10 years. The account earns 4.0% interestcompounded monthly. How much should she invest now to achieve that goal? Answer:

Answer 1

Given:

• Final amount, A = $80,000

,

• Time, t = 10 years

,

• Interest rate, r = 4.0% = 0.04

,

• Number of times compounded, n = monthly = 12 times a year.

Let's find the amount she should invest to achieve her goal.

Here, we are to find the principal, P.

Apply the compound interest formula:

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

Where:

A = $80,000

r = 0.04

n = 12

t = 10 years

Substitute values into the formula and solve for P:

We have:

`\begin{gathered} 80000=P(1+(0.04)/(12))^(12*10) \\ \\ 80000=P(1.0033333)^(120) \\ \\ 80000=P(1.49083) \end{gathered}`

Divide both sides by 1.49083:

`\begin{gathered} (80000)/(1.49083)=(P(1.49083))/(1.49083) \\ \\ 53661.29=P \end{gathered}`

Therefore, the amount she should invest is $53,661.29

ANSWER:

$53,661.29