Problema Solution
Sam is planning on going on a holiday to Europe in 18 months’ time. He knows that he will need $6500 to be able to visit every country that he wants to. How much does Sam need to invest now in a term deposit which offers 6.2% p.a. interest compounded fortnightly so that he will have the required $6500 in 18 months’ time?
Answer provided by our tutors
P = the money needed to invest
r = 0.062 or 6.2% annual interest rate
t = 18 months = 1.5 years = 78 weeks
m = 52/2 = 26 compounding periods per year (since 1 year has 52 weeks and the interests is compounded fortnightly (every 2 weeks))
i = r/m = 0.062/26 interest rate per period
n = t*m = 1.5*26 = 39 total number of compounding periods
A = $6,500 the future value
A = P(1 + i)^n
6500 = P(1 + 0.062/26)^39
P = 6500/(1 + 0.062/26)^39
P = $5,923.41
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Sam should deposit $5,923.41.