Respuesta :
The person must invest the money in the bank for 18 years to reach $19600, if a person invests 9000 dollars in a bank and the bank pays 4.25% interest compounded daily.
Step-by-step explanation:
The given is,
A person invests 9000 dollars in a bank
The bank pays 4.25% interest compounded daily
Future amount $19600
Step:1
Formula to calculate the future investment with compounded daily,
[tex]A = P (1+\frac{r}{n})^{nt}[/tex]................................(1)
Where, A - Future amount
P - Initial investment
r - Interested rate
n - No.of times for a year
t - No.of years
Step:2
From the given values,
A = $ 19600
P = $ 9000
r = 4.25 %
n = 365 ( ∵ Compounded daily )
Equation (1) becomes,
[tex]19600 = 9000(1+\frac{0.0425}{365})^{365t}[/tex]
[tex]\frac{19600}{9000}= (1+0.000116438)^{365t}[/tex]
[tex]2.177778=(1.000116438)^{365t}[/tex]
( Take log on both sides )
[tex]log 2.17778= log (1.000116438)^{365t}[/tex]
[tex]log 2.17778=( 365t)log (1.000116438)[/tex]
Substitute the log values,
[tex]0.338014 = (365t)(0.000050565)[/tex]
[tex]\frac{0.338014}{0.000050565}= 365t[/tex]
[tex]6684.6842 = 365t[/tex]
[tex]t = \frac{6684.6842}{365}[/tex]
= 18.314
≅ 18 years
No.of years, t = 18 years
Result:
The person must invest the money in the bank for 18 years to reach $19600, if a person invests 9000 dollars in a bank and the bank pays 4.25% interest compounded daily.
It will take approximately 18.4years for the person to make 19600
The formula for calculating the compound amount is expressed as:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex] where:
A is the amount
P is the amount invested
n is the compounding amount
t is the time taken
Given the following parameters
A = 19600
P = 9000
r = 4.25% = 0.0425
n = 365 (compounded daily)
Substitute the given parameters into the formula to get the time "t"
[tex]19600 = 9000(1+\frac{0.0425}{365} )^{365t}\\2.1778 = (1+0.0001164)^{365t}\\2.1778 = (1.0001164)^{365t}\\log2.1778 = 365tlog(1.0001164)\\0.3380 = 0.0184t\\t = \frac{0.3380}{0.0184} \\t \approx 18yrs[/tex]
Hence it will take approximately 18.4years for the person to make 19600
Learn more here: https://brainly.com/question/18456266
