Janet dreams to go on vacation in three years. How much should she invest now so that she will have $15,000 by that time if the account earns 1 3/8% compounded quarterly?
P(1+0.01375/4)^(4*3) = 15000
AKA $14,394.86
To determine how much Janet should invest now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future amount (in this case, $15,000)
P = the principal amount (the initial investment we're trying to find)
r = the annual interest rate (1 3/8% can be expressed as a decimal, which is 1.375% or 0.01375)
n = the number of times the interest is compounded per year (quarterly compounding implies 4 times a year)
t = the number of years (3 years in this case)
Now, we can substitute these values into the formula and solve for P:
$15,000 = P(1 + 0.01375/4)^(4*3)
To simplify the calculation, let's solve the exponent first:
(1 + 0.01375/4)^(4*3) = (1 + 0.0034375)^12 ≈ 1.04243
Now we can rewrite the equation:
$15,000 = P * 1.04243
Finally, solving for P:
P = $15,000 / 1.04243 ≈ $14,403.78
Therefore, Janet should invest approximately $14,403.78 now to have $15,000 in three years if the account earns 1 3/8% compounded quarterly.