Question

In an effort to save money for early retirement, an environmental engineer plans to deposit $1200 per month starting one month from now, into a self-directed investment account that pays 8% per year compounded semiannually. How much will be in the account at the end of 25 years

Answer 1

To calculate the amount in the account at the end of 25 years, use the formula for compound interest with the given values.

Step-by-step explanation:

To calculate the amount in the account at the end of 25 years, we can use the formula for compound interest:

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

Where:

• A is the future value of the investment
• P is the principal amount, which is $1200 per month
• r is the annual interest rate, which is 8%
• n is the number of times the interest is compounded per year, which is semiannually, so n = 2
• t is the number of years, which is 25

Plugging in the values into the formula:

A = 1200
`(1 + 0.08/2)^((2*25))`

Simplifying the equation:

A = 1200
`(1 + 0.04)^((50))`

A =
`1200(1.04)^((50))`

Using a calculator, the future value of the investment at the end of 25 years is approximately $9,470.52.

Answer 2

$1,099,203.00

Step-by-step explanation:

In this question we have to find out the future value that is shown in the attachment below:

Provided that

Present value = $0

Rate of interest = 8% ÷ 2 = 4%

NPER = 25 years × 2 = 50 years

PMT = $1,200 × 6 months = $7,200

The formula is shown below:

= -FV(Rate;NPER;PMT;PV;type)

So, after solving this, the future value is $1,099,203.00