mario borrows $12,000 from his uncle for a business venture. some of the conditions of the loan are…

mario borrows $12,000 from his uncle for a business venture. some of the conditions of the loan are unusual.\n- the loan is set up for 5 years, at 7% interest, compounded monthly.\n- mario is not required to make any payments during the 5 years; however, full payment, with interest, is due at the end of the 5 years.\nif mario makes no payments until the end of the 5 years, which equation represents the total amount mario must pay his uncle?\na $a = 12000(1 +.07)^{60}$\nb $a = 12000(1+\frac{.07}{5})^{(5)(12)}$\nc $a = 12000(1+\frac{.07}{12})^{5}$\nd $a = 12000(1+\frac{.07}{12})^{(5)(12)}$

mario borrows $12,000 from his uncle for a business venture. some of the conditions of the loan are unusual.\n- the loan is set up for 5 years, at 7% interest, compounded monthly.\n- mario is not required to make any payments during the 5 years; however, full payment, with interest, is due at the end of the 5 years.\nif mario makes no payments until the end of the 5 years, which equation represents the total amount mario must pay his uncle?\na $a = 12000(1 +.07)^{60}$\nb $a = 12000(1+\frac{.07}{5})^{(5)(12)}$\nc $a = 12000(1+\frac{.07}{12})^{5}$\nd $a = 12000(1+\frac{.07}{12})^{(5)(12)}$

Answer

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Identify the values given

We have $P=$12000$, $r = 0.07$ (since $7%=0.07$), $n = 12$ (compounded monthly), and $t = 5$ years.

Step3: Substitute values into the formula

Substitute $P = 12000$, $r=0.07$, $n = 12$, and $t = 5$ into the formula $A = P(1+\frac{r}{n})^{nt}$. We get $A=12000(1 +\frac{0.07}{12})^{(12\times5)}$.

Answer:

D. $A = 12000(1+\frac{0.07}{12})^{(5)(12)}$