1. ## finace

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

2. Hello, Gracy!

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

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

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

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

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

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

Therefore, you should deposit $\displaystyle \boxed{\$245.78}$* each quarter. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ * Note that we round up. If we deposit$\displaystyle \$245.77$ each quarter,
. . the final amount will be only $\displaystyle \$9,999.96$ii) What quarterly deposit is required if the money earns 4% per annum, compounded quarterly? Use the same formula with: .$\displaystyle A = 10,000,\;i = \frac{4\%}{4} = 0.01,\;n = 32\$