compound interest formulas\nthe interest of a compound interest investment or loan can be computed with the…
compound interest formulas\nthe interest of a compound interest investment or loan can be computed with the formula\ni = a - p (where a is given below).\nthe end amount of a compound interest investment or loan can be computed with the formula\na = p(1 + \\frac{r}{n})^{nt}.\nuse these formulas to evaluate the amounts indicated below.\nlet p = $3,500, r = 8.2%, n = 4, and t = 11 years. determine the interest, i, at the end of 11\nyears.\ninterest = $ 5047.53 √\ndollars\nlet p = $4,200, r = 12.3%, n = 12, and t = 3 years. determine the total end amount, a, at the\nend of 3 years.\nend amount = $\n\ndollars\nquestion help: video read message instructor
Answer
Explanation:
Step1: Identify the compound - interest formula
The formula for the end - amount of a compound interest investment 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: Convert the interest rate to decimal
Given $r = 12.3%=0.123$, $P = 4200$, $n = 12$, and $t = 3$.
Step3: Substitute the values into the formula
$A=4200\times(1 +\frac{0.123}{12})^{12\times3}$. First, calculate the value inside the parentheses: $\frac{0.123}{12}=0.01025$, then $1+\frac{0.123}{12}=1 + 0.01025=1.01025$. Next, calculate the exponent: $12\times3 = 36$. So, $A = 4200\times(1.01025)^{36}$.
Step4: Calculate $(1.01025)^{36}$
Using a calculator, $(1.01025)^{36}\approx1.43077$.
Step5: Calculate the end - amount $A$
$A=4200\times1.43077 = 6009.234\approx6009.23$.
Answer:
$6009.23$