## Related questions with answers

Question

For the following exercises, determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate. Deposit amount: $100; total deposits: 120; interest rate: 10%, compounded semi-annually

Solution

VerifiedStep 1

1 of 2The given annuity problem describes a geometric sequence with $a_1= 100$, $n= 120$ and $r= 1+\dfrac{.1}{2}=1.05$. Using $S_n=\dfrac{a_1(1-r^n)}{1-r}$ or the formula for a finite geometric series, then

$\begin{align*} S_n&=\dfrac{a_1(1-r^n)}{1-r} \\\\ S_{120}&=\dfrac{100(1-(1.05)^{120})}{1-1.05} \\\\&\approx 695823.97 .\end{align*}$

Hence, the total amount after $120$ deposits is $\$695,823.97$.

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