Question

Mrs. Stevens wants to have 18,000 in the bank in 3 years. If she deposits $9500 today at 4% compounded quarterly for 3 years, how much additional money will she need to add after 3 years to her investment to make her balance $18000

Answer 1

`\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$9500\\ r=rate\to 4\%\to (4)/(100)\to &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly means} \end{array}\to &4\\ t=years\to &3 \end{cases} \\\\\\ A=9500\left(1+(0.04)/(4)\right)^(4\cdot 3) \\\\\\ \textit{the difference willl then be}\qquad 18000 - A`

and 18000 - A is how much more she needs to make 18000

Answer 2

$7259.16

Explanation:

Hello

you can use the compound interest formula

`A=P*(1+(r)/(n) )^(t) \\\\`

wherem A is the accumulated amount, P is the principal or initial amount, r is the interest rate and t is the number of periods

`t=number of period = 3 years ((4 quartely)/(1 year) )=12 periods\\A=9500*(1+(0.04)/(4) )^(12) \\\\A=9500*(1.01^(12) )\\A= $10704.83\\\\she will need to add B\\\\B=18000-A\\B=18000-10704.83\\B=$7259.16`

Have a great day