Respuesta :
Given:
The rate of interest is, r = 7.5% = 0.075.
The required total amount is, A = $15,000.
The number of years, t = 6 years.
The objective is to find the principal amount required to invest.
Explanation:
The general formula of compound interest is,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here, n represents the number of times the interest is compounded.
It is given that the interest is compounded monthly, so the value of n = 12.
To find principal amount:
Substitute the given values in the above formula.
[tex]\begin{gathered} 15000=P(1+\frac{0.075}{12})^{12(6)} \\ P=\frac{15000}{(1+0.00625)^{72}} \\ P=9577.83 \end{gathered}[/tex]To find APY:
The annual principal yield can be calculated as,
[tex]\begin{gathered} \text{APY}=(1+\frac{r}{n})^n-1 \\ =(1+\frac{0.075}{12})^{12}-1 \\ =0.0776 \end{gathered}[/tex]To find percent change:
The percent change can be calculated as,
[tex]\begin{gathered} \text{\%change}=\frac{A-P}{P}\times100 \\ =\frac{15000-9577.83}{9577.83}\times100 \\ =\frac{5422.17}{9577.83}\times100 \\ =0.5661167\ldots.\times100 \\ =56.61\text{ \%} \end{gathered}[/tex]Hence,
The principal money to be invested in the account is $ 9577.83.
The Annual Percent Yield is 0.0776.
The percent change for 6 year is 56.6%.
