Hey guys, i need with this.
To make $20,000 in 3 years, Sally decides to make 6 equal deposits in an account at 6-monthly intervals starting now. If the interest rate is 11% per annum compounded semi-annually, how much is each deposit?
Hey guys, i need with this.
To make $20,000 in 3 years, Sally decides to make 6 equal deposits in an account at 6-monthly intervals starting now. If the interest rate is 11% per annum compounded semi-annually, how much is each deposit?
Hello, Steve!
To make $20,000 in 3 years, Sally decides to make 6 equal deposits
in an account at 6-monthly intervals starting now.
If the interest rate is 11% per annum compounded semi-annually,
how much is each deposit?
This is an Annuity problem.
If you're not familiar with the formula, you're in deep weeds . . .
Annuity formula: . $\displaystyle A \;=\;D\,\frac{(1+i)^n-1}{i}$
. . where: .$\displaystyle \begin{Bmatrix}A &=& \text{final amount} \\ D &=& \text{periodic deposit} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}$
We have: .$\displaystyle A = 20,000,\; i = \frac{11\%}{2} = 0.055,\;n = 6 $
. . and we might as well solve for $\displaystyle D\!:\;\;D \;=\;A\,\frac{i}{(1+i)^n-1} $
So we have: .$\displaystyle D \;=\;20,000\,\frac{0.055}{(1.055)^6-1} \;=\;2903.578952$
Therefore, Sally should deposit $2903.58 each time.
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