Hao made a single investment which,after 5 years invested at 12% compounded semiannually,has accumulated to $214,900.How much did Hao invest initially? (PV of $1,FV of $1,PVA of $1,and FVA of $1)$\bold{\text{(Use appropriate factor(s)from the tables provided.)}}$
A)$214,896
B)$160,584
C)$211,476
D)$120,000
E)$ 21,486

Question

Quizplus · Accepted Answer

The future value (FV) of an investment is calculated using the formula $FV = PV(1 + \frac{r}{n})^{nt}$, where PV is the present value (initial investment), r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years. Given a 12% annual interest rate compounded semiannually for 5 years, we have $r = 0.12$, $n = 2$, and $t = 5$. The future value is given as $214,900. We need to solve for PV.Rearranging the formula to solve for PV gives us $PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}$.Substituting the given values: $PV = \frac{214,900}{(1 + \frac{0.12}{2})^{2*5}}$.This simplifies to $PV = \frac{214,900}{(1 + 0.06)^{10}}$.Calculating this gives us $PV = \frac{214,900}{1.790847}$.Therefore, $PV ≈ 120,000$.This calculation shows that Hao initially invested approximately $120,000.

Hao Made a Single Investment Which,after 5 Years Invested at 12