Solve the problem.
-The formula $S = A \left( \frac { ( 1 + r ) ^ { t } + 1 - 1 } { r } \right)$ models the value of a retirement account, where $A =$ the number of dollars added to the retirement account each year, $\mathrm { r } =$ the annual interest rate, and $\mathrm { S } =$ the value of the retirement account after t years. If the interest rate is $7 \%$, how much will the account be worth after 15 years if $\$ 800$ is added each year? Round to the nearest whole number.
A) $\$ 22,310$
B) $\$ 2347$
C) $\$ 12,800$
D) $\$ 35,316$

Question

Quizplus · Accepted Answer

The formula given is a slight modification of the future value of a series formula. Plugging in the values: $A = 800$, $r = 0.07$, and $t = 15$, we calculate $S = 800 \left( \frac{(1 + 0.07)^{15} - 1}{0.07} \right)$, which approximates to \(\$22,310 when rounded to the nearest whole number.

Solve the Problem S=A((1+r)t+1−1r)S = A \left( \frac { ( 1 + r ) ^ { t } + 1 - 1 } { r } \right)S=A(r(1+r)t+1−1​)

Solve the Problem $S = A \left( \frac { ( 1 + r ) ^ { t } + 1 - 1 } { r } \right)$