What single amount deposited now into an account paying $9 \frac { 2 } { 3 } \%$ annual interest, compounded quarterly, would fund an annuity paying $\$ 3,050$ quarterly for the next 29 years?
A) $\quad \$ 118,273.49$
B) $\$ 118,318.61$
C) $\quad \$ 118,298.49$
D) $\quad \$ 118,448.28$

Question

Quizplus · Accepted Answer

We can use the formula $A=\dfrac{P(i+n)^n}{(1+i)^n-1}$, where $A$ is the annuity payment, $P$ is the initial deposit, $i$ is the quarterly interest rate (converted to a decimal), and $n$ is the total number of quarters (29 years = 116 quarters).

Plugging in the given values, we get $3050=\dfrac{P(0.0925+1)^{116}}{(1+0.0925)^{116}-1}$. Solving for $P$, we get $P=\boxed{	extbf{(C)}\ \$118,298.49}$.

What Single Amount Deposited Now into an Account Paying 923%9 \frac { 2 } { 3 } \%932​%

What Single Amount Deposited Now into an Account Paying $9 \frac { 2 } { 3 } \%$