Question

Caleb invested $80,000 in an account paying an interest rate of 5.4% compounded monthly. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 13 years?

Answer 1

Answer:

$\large \boxed{\text{\ 161 170}}$

Step-by-step explanation:

The formula for the amount (A) accrued  on an investment earning compound interest is

$A = P(1 + \frac{r}{n})^{nt}$

where

P = the amount of money invested (the principal)

r = the annual interest rate expressed as a decimal fraction

t = the time in years

n = the number of compounding periods per year

Data:

P = $80 000

r =  5.4 % = 0.054

t = 13 yr

n = 12 /yr

Calculation:

$\begin{array}{rcl}A& =& P \left (1 + \frac{r}{n} \right )^{nt}\\& =& 80000 \left(1 + \dfrac{0.054}{12} \right )^{12\times13}\\\\& =& 80000 (1 + 0.0045 )^{156}\\& =& 80000 (1.0045)^{156}\\& =& 80000 \times 2.01461\\& =& \mathbf{161170}\\\end{array}\\\text{The account would contain \large \boxed{\textbf{\ 161 170}} }$