An investment has grown to $89,000 over a 6-year period. The interest was computed daily and the rate was 7 3/8% per year. What was the original investment?
X(1+.07375/365)^6*365=89,000
X(1+.000202)^2,190=89,000
X(1.000202)^2,190=89,000
X*1.556=89,000
X=89,000/1.556
X=$57,197.94 WAS THE ORIGINAL INVESTMENT
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To find the original investment, we can use the compound interest formula.
The compound interest formula is given by:
A = P(1 + r/n)^(nt)
Where:
A = the final amount or value
P = the principal or original investment
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, we are given:
A = $89,000 (the final amount)
r = 7 3/8% per year, which can be written as 7.375% or 0.07375 (expressed as a decimal)
n = 365 (since interest is compounded daily)
t = 6 years
Substituting these values into the formula, we get:
$89,000 = P(1 + 0.07375/365)^(365*6)
Next, we can solve for P by isolating it on one side of the equation.
Dividing both sides of the equation by (1 + 0.07375/365)^(365*6), we have:
P = $89,000 / (1 + 0.07375/365)^(365*6)
Calculating this expression will give us the original investment.