Using compound interest, it is found that it will take 62.91 years for the account to earn $7500.
Compound interest,
A(t) = P × [tex](1 + \frac{r}{n} )^{nt}[/tex]
The amount of cash after t years is A(t).
The principal is P. (the initial sum of money).
The interest rate is r. (as a decimal value).
The number of times interest is compounded quarterly is n.
t is the number of years that the money will be invested or lent out for.
P = $2500
r = 1.75% = 0.0175
n = 4
A(t) = $7500
then enter the values as follows:
A(t) = P × [tex](1 + \frac{r}{n} )^{nt}[/tex]
$7500 = $2500 × [tex](1 + \frac{0.0175}{4} )^{4t}[/tex]
$7500 ÷ $2500 = [tex](1 + \frac{0.0175}{4} )^{4t}[/tex]
$3 = [tex](1.004375)^{4t}[/tex]
Log3 = 4t log(1.004375) after applying the log on both sides.
t = log3 ÷ (4log(1.004375))
t = 62.91
Kevin will earn $7500 for 62.91 years.
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