To help pay for a class trip at the end of the senior year, the junior class at a high school invests $1800 from a fund-raiser in a 18-month CD paying 2.6% interest compound monthly. Determine the amount the class will receive when it cashes in the CD after 18 months.
To determine the amount the class will receive when it cashes in the CD after 18 months, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given:
P = $1800
r = 2.6% = 0.026 (as a decimal)
n = 12 (compounded monthly)
t = 18/12 = 1.5 years
Using the formula:
A = 1800(1 + 0.026/12)^(12*1.5)
Calculating the expression inside the parentheses:
A = 1800(1 + 0.026/12)^(12*1.5)
= 1800(1 + 0.0021666667)^(12*1.5)
= 1800(1.0021666667)^(18)
Using a calculator or spreadsheet:
A ≈ 1800(1.0021666667)^18
A ≈ 1800 * 1.0386384984
A ≈ $1870.15
Therefore, the class will receive approximately $1870.15 when they cash in the CD after 18 months.
To determine the amount the class will receive when they cash in the CD after 18 months, we can use the formula for compound interest:
\(A = P(1 + \frac{r}{n})^{nt}\)
Where:
A = the final amount
P = the principal amount (in this case, $1800)
r = the annual interest rate (in decimal form, 2.6% = 0.026)
n = the number of times interest is compounded per year (monthly compound requires n = 12)
t = the number of years (in this case, 18 months = 1.5 years)
Substituting the given values into the formula, we have:
\(A = 1800(1 + \frac{0.026}{12})^{12 \cdot 1.5}\)
Using a calculator, we can then calculate the value of A:
\(A = 1800(1 + \frac{0.026}{12})^{18}\)
\(A \approx 1800 \cdot 1.02603843183^{18}\)
\(A \approx 1800 \cdot 1.04974216906\)
\(A \approx 1889.53\)
Therefore, when the class cashes in the CD after 18 months, they will receive approximately $1889.53.