Based on the calculation below, the number of years it would be for Mia to have $34,000 is 29.1 years.
How do we find the period or time of investment?
The formula in the question is the formula for calculating the future value of an ordinary annuity and it can be rewritten as follows:
A = d((((1 + i)^n) – 1) / i) …………………………… (1)
Where:
A = $34,000
d = $850
i = 0.4% * number of months in a year = 0.4% * 12 = 4.8% = 0.048
n = number of years?
Substitute all the values into equation (1) and solve for n, we have:
$34,000 = $850((((1 + 0.048)^n) - 1) / 0.048)
$34,000 / $850 = (((1 + 0.048)^n) - 1) / 0.048
40 = (((1 + 0.048)^n) - 1) / 0.048
40 * 0.048 = ((1 + 0.048)^n) – 1
1.92 + 2 = (1 + 0.048)^n
3.92 = 1.048^n
Taking the log of both sides, we have:
Log3.92 = nlog1.048
0.593286067020457 = n 0.0203612826477079
n = 0.593286067020457 / 0.0203612826477079
n = 29.1379515370189
Rounding to the nearest of a year, we have:
n = 29.1
Learn more about the future value of an ordinary annuity here: https://brainly.com/question/17925440.
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