An investor makes deposits of $R every 2 weeks into a fund paying interest at j₄ = 6%.At the time of the 130^th deposit,she wishes to have accumulated $50,000.What is R?

Question

Quizplus · Accepted Answer

We can use the formula for the future value of an annuity:

$FV = R\frac{(1 + r)^n - 1}{r}$

Where:
FV = future value of the annuity
R = the periodic deposit (unknown)
r = the interest rate per deposit period (6% / 26 = 0.230769%)
n = number of deposit periods (130)

Plugging in the numbers:

$50,000 = R\frac{(1 + 0.00230769)^{130} - 1}{0.00230769}$

$50,000 = R\frac{1.063717^ {130} - 1}{0.00230769}$

$50,000 = R\frac{1.786984 - 1}{0.00230769}$

$50,000 = R\frac{0.786984}{0.00230769}$

$R = 330.57$

Therefore, the answer is B) $330.57.

An Investor Makes Deposits of $R Every 2 Weeks into a Fund