Respuesta :
Using compound interest, it is found that he must invest his money at a rate of 8.78% a year.
What is compound interest?
The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
- 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.
In this problem, the parameters are as follows:
t = 3, A(t) = 60000, P = 46150.3, n = 12.
Hence:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]60000 = 46150.3\left(1 + \frac{r}{12}\right)^{12 \times 3}[/tex]
[tex]\left(1 + \frac{r}{12}\right)^{36} = 1.3[/tex]
[tex]\sqrt[36]{\left(1 + \frac{r}{12}\right)^{36}} = \sqrt[36]{1.3}[/tex]
[tex]1 + \frac{r}{12} = (1.3)^{\frac{1}{36}}[/tex]
[tex]1 + \frac{r}{12} = 1.00731451758[/tex]
[tex]\frac{r}{12} = 0.00731451758[/tex]
r = 12 x 0.00731451758
r = 0.0878.
He must invest his money at a rate of 8.78% a year.
More can be learned about compound interest at https://brainly.com/question/25781328
