GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: On January 1, 1994, Jill invested P dollars in an account that pays in
[#permalink]
27 Jan 2023, 11:18
Knowing the formula for compound interest helps a lot here.
Compound interest is given by
\(A = P(1 +\frac{r}{n})^{nt}\)
A = final amount
P = principal invested
r = interest rate in decimal form
n = number of compounding periods per year
t = time
Here interest compounds annually; it earns "interest on interest," and pays one time per year, on December 31.
So r = .08
Because \(n = 1\), \((\frac{.08}{1}) = .08\)
Then \(1 + .08 = 1.08\)
Time t, = 4 years: she gets paid December 31 of 1994, 1995, 1996, and 1997
Where n = 1 and t = 4, thus: \((1.08)^{1*4} = (1.08)^4\)
Finally, multiply by the principal: \(P(1.08)^4\)
Answer: D