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Sagot :
For the money to grow to $60,000, It will take 4 years.
The formula for calculating Compound Interest is
[tex]A = P(1+\frac{r}{n} )^n^t[/tex]
P is the original amount you borrow or deposit, or the primary amount.
r is the interest rate per year.
t is the number of years over which the deposit or loan is made.
A is the total amount of money after n years, including interest.
There are n times each year that interest is compounded.
A = $60,000
P = $45,000
r = 8% = 0.08
n = 4
We are to look for t = number of years the amount is deposited or borrowed for
[tex]60,000 = 45,000 (1+\frac{0.08}{4} )^4^t[/tex]
[tex]60,000= 45,000 (1.02)^4^t[/tex]
[tex]\frac{60,000}{45,000}=(1.02)^4^t[/tex]
[tex]1.33 = (1.02)^4^t[/tex]
Simply into exponential on both sides,
[tex](1.02)^{14.40} = (1.02)^{4t} \\[/tex]
use logarithms on both sides
[tex]In(1.02)^{14.40} = In(1.02)^{4t} \\[/tex]
[tex]{14.40} \times In(1.02) = 4t \times In(1.02) \\[/tex]
Divide by In(1.02) on both sides
[tex]4t = 14.40[/tex]
[tex]t=\frac{14.40}{4} \\\\t = 3.6[/tex]
Rounding off nearest to the whole number = 4 years
Thus, It will take around 4 years for the money to grow to $60,000.
To learn more about Interest, visit the link below:
brainly.com/question/14213579
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