Question

To help with his retirement savings, Dan has decided to invest. Assuming an interest rate of 3,43% compounded quarterly, how much would he have to invest

to have $148,700 after 18 years?
Do not round any intermediate computations, and round your final answer to the nearest dollar. If necessary, refer to the list of financial formulas.
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Answer 1

He would have to invest $80,412.

Explanation:

Compound interest:

The compound interest formula is given by:

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

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Assuming an interest rate of 3,43% compounded quarterly.

This means that
`r = 0.0343, n = 4`

How much would he have to invest to have $148,700 after 18 years?

This is P for which
`t = 18, A(t) = 148700`. So

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

`148700 = P(1 + (0.0343)/(4))^(72)`

`P = (148700)/((1 + (0.0343)/(4))^(72))`

`P = 80412`

He would have to invest $80,412.