Answer:
2.5 years
Step-by-step explanation:
Amount= $8036
Principal= $7000
Rate =5.6%
t= ?
n= 2
A= P(1 + r/n)^nt
8036= 7000(1 + 0.028)^2t
1.148= (1 + 0.028)^2t
log(1.148) = log (1 + 0.028)^2t
0.05994= 2t × 0.01199
t= 2.5 years
It will take t = 2.5 years for the account to grow to $8036.
Given that,
Total saving amount = $7000
Annual rate = 5.6% = 0.056
We have to determine,
Assuming that no withdrawals are made, how long will it take for the account to grow to $8036.
According to the question,
Amount = $8036
Principal = $7000
Rate = 0.056
n = 2
To find the value of time t calculation done in single unit,
[tex]A = P (1+ \frac{r}{n} )^{nt} \\\\8036 = 7000 (1+\frac{0.056}{2})^{2t} \\\\\frac{8036}{7000} = (1+0.028})^{2t} \\\\1.148 = (1+0.028)^{2t} \\\\[/tex]
Taking log on both sides,
[tex]log(1.148) = log(1+0.028)^{2} \\\\0.0599 = 2t\times0.0119\\\\\frac{0.599}{0.022} = t\\\\t = 2.5 years[/tex]
Hence, It will take t = 2.5 years for the account to grow to $8036.
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