finace

Hello, Gracy!

Is someone assigning these problems without teaching you the necessary formula?

Quote:

You need $10,000 in 8 years.
i) What amount should you deposit at the end of each quarter at 6% per annum,
compounded quarterly, so that you will have the required $10,000?

This is an Annuity problem, which has this formula: . $A \;= \;D\,\frac{(1 + i)^n - 1}{i}$

. . where: . $\begin{array}{cccc} A &=& \text{final amount}\\ D & = &\text{periodic deposit} \\ i & = & \text{periodic interest rate} \\ n & = & \text{number of periods}\end{array}$

Solve for $D:\;\;D \;= \;A\,\frac{i}{(1+i)^n - 1}$

You have: . $A = 10,000,\;i = \frac{6\%}{4} = 0.015,\;n = 32$

Hence: . $D \;= \; 10,000\,\frac{0.015}{1.015^{32} - 1} \;=\;245.7709697$

Therefore, you should deposit $\boxed{\$245.78}$ * each quarter.

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* Note that we round up.

If we deposit $\$245.77$ each quarter,
. . the final amount will be only $\$9,999.96$

Quote:

ii) What quarterly deposit is required if the money earns 4% per annum,
compounded quarterly?

Use the same formula with: . $A = 10,000,\;i = \frac{4\%}{4} = 0.01,\;n = 32$