15 2 pts Suppose you want to be able to save 10 000 by the t

15. (2 pts) Suppose you want to be able to save $10, 000 by the time that you graduate four years from now. If von plan to invest in an account that earns 5% interest compounded annually. how large will your initial investment have to be?

Solution

A = P(1 + r_/n)^nt ,A is the amount after t years.P is the initial amount, r is the annual rate of interest, n= number of times compounded in year

A=10000, r=5%=0.05 , n=1, t=4

=>10000=P(1+ 0.05_/1)^1*4

=>10000=P(1+ 0.05)⁴

=>P=10000_/(1.05)⁴

=>P=8227

initial investment has to be $ 8227 approximately

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