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Sagot :
Answer:
The amount is $8358.7 and the interest is $3858.7.
Step-by-step explination
STEP 1: To find amount we use formula:
A = P
1 +
r
n
n·t
A = total amount P = principal or amount of money deposited, r = annual interest rate n
= number of times compounded per year t = time in years In this example we have
P = $4500 , r = 7% , n = 2 and t = 9 years
After plugging the given information we have
A = 4500
1 +
0.07
2
2·9
A = 4500 · 1.03518
A = 4500 · 1.857489
A = 8358.7
STEP 2: To find interest we use formula A = P + I, since A = $8358.7 and P = $4500 we
have:
A = P + I
8358.7 = 4500 + I
I = 8358.7 − 4500
I = 3858.7
The person must leave the money in the bank for 11.8 years so that it reaches the value of 1600 dollars.
What is compound interest?
Compound interest is the addition of interest on the interest of the principal amount. It is given by the formula,
[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]
where A is the final amount,
P is the principal amount,
r is the rate of interest,
n is the period after which the amount is compounded, and
t is the number of years after which the amount is compounded.
We know the formula of compound Interest, also it is given that the person invests $1,000(P) at an interest rate of 4%(r) compounded quarterly. Therefore, the formula can be written as,
[tex]A = P(1+\dfrac{r}{n})^{nt}[/tex]
Since the amount is compounded quarterly, therefore, the value of n is 4.
[tex]1600 = 1000(1+\dfrac{0.04}{4})^{4t}\\\\1.6 = (1+0.01)^{4t}\\\\1.6 = 1.01^{4t}\\\\\rm log_{1.01}1.6 = 4t\\\\47.235 =4t\\\\t = 11.8[/tex]
Hence, the person must leave the money in the bank for 11.8 years so that it reaches the value of 1600 dollars.
Learn more about Compound Interest:
https://brainly.com/question/25857212
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