Problema Solution
Samantha Wimberly is planning a vacation in Europe in 4 years, after graduation. She estimates that she will need $3,500 for the trip.
If her bank is offering 4-year certificates of deposit with 8% interest compounded she quarterly, how much must Samantha invest now to have the money for the trip?
Answer provided by our tutors
Compound amount
A = P(1 + i)^n
A = $3,500 is the future (maturity) value
r = 0.08 is the annual interest rate of 8%
m = 4 is the number of compounding periods per year since it is compounded quarterly
t = 4 years
n = mt = 4*4 = 16 is the number of compounding periods
i = r/m = 0.08/4 = 0.02 is the interest rate per period
we need to find P the principal or how much must Samantha invest
A = P(1 + i)^n => P = A/((1 + i)^n)
P = 3500/((1 + 0.02)^16)
P = $2,549.56
Samantha must invest $2,549.56 to have the money for the trip in 4 years.