TheMechanic
On January 1, 1994, Jill invested P dollars in an account that pays interest at a rate of 8 percent per year, compounded annually on December 31. If there were no other deposits or withdrawals in the account, how many dollars were in the account on January 1, 1998, in terms of P?
A) \(0.32P\)
B) \(4.32P\)
C) \((0.08)^4P\)
D) \((1.08)^4P\)
E) \((1.08P)^4\)
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