Myrna Lewis wishes to have $4,000 in four years to tour Europe. How much must she invest today at 8% interest compounded quarterly to have $4,000 in four years?
$4000 = x(1+ 0.02)^16
=$2,913.78
To find out how much Myrna Lewis must invest today at 8% interest compounded quarterly to have $4,000 in four years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($4,000)
P = the principal amount to be invested today (unknown)
r = the annual interest rate (8%, or 0.08)
n = the number of times the interest is compounded per year (quarterly, so n = 4)
t = the number of years the money is invested for (4 years)
To isolate the principal amount P, we can rearrange the formula as follows:
P = A / (1 + r/n)^(nt)
Plugging in the known values:
P = 4000 / (1 + 0.08/4)^(4*4)
Simplifying the equation within the parentheses:
P = 4000 / (1 + 0.02)^16
Calculating the value within the parentheses:
P = 4000 / (1.02)^16
Evaluating (1.02)^16:
P = 4000 / 1.357911
Calculating the final value:
P ≈ $2,953.26
Therefore, Myrna Lewis must invest approximately $2,953.26 today at 8% interest compounded quarterly to have $4,000 in four years.