Respuesta :
Answer:
It will take a time of 24.65 year.
Step-by-step explanation:
The principal amount invested by person ( P ) = $300.
The annual rate of interest ( r ) = 3.45 %.
The amount or future value ( A ) = $700.
We have to find the time ( t ) when his future value becomes $700.
Given that interest compounded quarterly, n = 4.
Now using the compound interest formula,
A = P * [tex](1 + \frac{r}{n} )^{n*t}[/tex]
[tex]700 = 300 * ( 1 + \frac{0.0345}{4} )^{4 * t}[/tex]
2.3333 = [tex]( 1 + \frac{0.0345}{4} )^{4 * t}[/tex]
Taking log both sides.
[tex]log2.333 = log ( 1 + \frac{0.0345}{4} )^{4 * t}[/tex]
0.3679 = (4 * t ) * log 1.008625
0.3679 = 4 * t * 0.003729
t = 24.65 year.
Answer: it will take 24.6 years
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
A = 700
P = 300
r = 3.45% = 3.45/100 = 0.0345
n = 4 because it was compounded 4 times in a year.
t = 6 months = 6/12 = 0.5 year
Therefore,.
700 = 300(1 + 0.0345/4)^4 × t
700/300 = (1 + 0.008625)^4t
2.33 = (1.008625)^4t
Taking log of both sides,
Log 2.33 = 4t × og 1.008625
0.367 = 0.0149t
t = 0.367/0.0149
t = 24.6 years
