Full solution

Q. Ms. Donose decided to put

\$ 1500

into a savings account that earns

2.5 \%

interest compounded semi-annually. Using the equation

A=P\left(1+\frac{r}{n}\right)^{n t}

, find out how much money she will have after

29

years.

Identify Variables: Identify the variables from the problem. $\newline$ P = principal amount (initial deposit) = $\$1500$ $\newline$ r = annual interest rate in decimal = $2.5\%$ = $0.025$ $\newline$ n = number of times the interest is compounded per year = $2$ (semi-annually) $\newline$ t = number of years the money is invested = $29$
Plug into Formula: Plug the identified variables into the compound interest formula. $\newline$ $A = P(1 + \frac{r}{n})^{(nt)}$ $\newline$ $A = 1500(1 + \frac{0.025}{2})^{(2\cdot29)}$
Calculate Inside Parentheses: Calculate the values inside the parentheses. $\newline$ $1 + \frac{r}{n} = 1 + \frac{0.025}{2}$ $\newline$ $1 + \frac{r}{n} = 1 + 0.0125$ $\newline$ $1 + \frac{r}{n} = 1.0125$
Calculate Exponent: Calculate the exponent. $\newline$ $nt = 2 \times 29$ $\newline$ $nt = 58$
Substitute Values: Substitute the values back into the formula. $\newline$ $A = 1500(1.0125)^{58}$
Calculate Amount: Calculate the amount $A$ using the values. $\newline$ $A = 1500 \times (1.0125)^{58}$ $\newline$ $A = 1500 \times (1.0125)^{58} \approx 1500 \times 3.3449$ $\newline$ $A \approx 5017.35$