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AlexFokin [52]
2 years ago
9

Mrs. Matthews wants to have $18,000 in the bank in 2 years. If she deposits $9000 today at 6% compounded quarterly for 2 years,

how much additional money will she need to reach the desired $18,000?
Mathematics
2 answers:
OverLord2011 [107]2 years ago
6 0
Depends if you want
1. find how much he will earn, find the differnce between that and 18000
2. see how much to invest till he will  get 18000


A=P(1+ \frac{r}{n})^{nt}

A=futre amount
P=present amout
r=rate in decimal
n=number of times per year ccompounded
t=time in years


1.
A=?
P=9000
r=0.06
n=4 (quarter means 4 times per year)
t=2
?=9000(1+ \frac{0.06}{4})^{(4)(2)}
?=9000(1+ 0.015)^{8}
?=9000(1.015)^{8}
?=10138.4 will be earned
18000-10138.4=7861.6 needed

2.
A=18000
P=9000+x
r=0.06
n=4 (quarter means 4 times per year)
t=2
18000=(9000+x)(1+ \frac{0.06}{4})^{(4)(2)}
18000=(9000+x)(1+ 0.015)^{8}
18000=(9000+x)(1.015)^{8}
divide both sides by 1.015^8
15978.8=9000+x
minus 9000 both sides
6978.8 needed




if he willnot be investing any more, he needs $7861.6 more
if he will invest more he will need to invest $6978.8 more




aleksandr82 [10.1K]2 years ago
4 0

Answer:

<h2>She needs additionally 7,861.57 to reach the desired 18,000.</h2>

Step-by-step explanation:

Compounded interest formula is

A=P(1+\frac{r}{n} )^{nt}

Where P is the principal, r is the interest rate in decimal number, n is the number of compounded periods within a year and t is time in years.

By given, we have

P=9,000\\t=2\\n=4\\r=0.06

Replacing all values, we have

A=P(1+\frac{r}{n} )^{nt}\\A=9000(1+\frac{0.06}{4} )^{4(2)}= 9000(1.015)^{8}\\ A=10138.43

After 2 years, Mrs. Matthews will have 10,138.43.

So, the difference she needs to reach 18,000 is

-10,138.43+18,000=7,861.57

Therefore, she needs additionally 7,861.57 to reach the desired 18,000.

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