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, $r =$ the annual interest rate, and $\mathrm { S } =$ the value of the retirement iccount after t years. If the interest rate is $6 \%$, how much will the account be worth after 10 years if $\$ 1600$ is added each year? Round to the nearest whole number.
A) $\$ 23,955$
B) $\$ 31,519$
C) $\$ 3021$
D) $\$ 17,600$

Question

Quizplus · Accepted Answer

The formula given is for the future value of a series of annuity payments. Plugging in the values $A = 1600$, $r = 0.06$, and $t = 10$, we calculate $S = 1600 \left( \frac{(1 + 0.06)^{10 + 1} - 1}{0.06} \right)$, which approximates to $\$23,955$, rounding 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 $S = A \left( \frac { ( 1 + r ) ^ { t + 1 } - 1 } { r } \right)$