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Compound interest is the adding of interest to the principle sum of a loan or deposit. The time it will take the account to reach $980 is 5.6 years.
What is compound interest?
Compound interest is the adding of interest to the principle sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out, so that interest is received on the principal plus previously collected interest in the next quarter.,
[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 number of times interest is charged in a year
t is the number of years
Given the initial amount in the account was $710, while the rate of interest is such that money doubles itself in 12 years. Therefore, the rate will be,
2(710) = 710(1+x)¹²
2 = (1+x)¹²
Taking log,
log₍ₓ₊₁₎2 = 12
(log 2) / log(x+1) = 12
(log 2)/12 = log(x+1)
0.025 = log (x+1)
Taking antilog,
1.059463 = x+ 1
x = 0.05946 = 5.9463%
Now, the time it will take the account to reach $980 is,
980 = 710(1+5.9463%)ⁿ
Taking Log,
[tex]\log_{1.059463}1.38 =n\\\\n = \dfrac{\log 1.38}{\log 1.059463}\\[/tex]
n = 5.57956 ≈ 5.6 years
Hence, the time it will take the account to reach $980 is 5.6 years.
Learn more about Compound Interest:
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