Respuesta :
Answer:
He would have to invest $80,412.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
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 [tex]r = 0.0343, n = 4[/tex]
How much would he have to invest to have $148,700 after 18 years?
This is P for which [tex]t = 18, A(t) = 148700[/tex]. So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]148700 = P(1 + \frac{0.0343}{4})^{72}[/tex]
[tex]P = \frac{148700}{(1 + \frac{0.0343}{4})^{72}}[/tex]
[tex]P = 80412[/tex]
He would have to invest $80,412.
