Question 1186448: Find the amount owed on an investment of P 10,000 into a money market account that pays a simple interest rate of 1.75% over a 39-week period.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! simple interest formula is:
i = p * r * t
f = p + i
replace i with p * r * t and you get:
f = p + p * r * t
if you factor out the p, you get:
f = p * (1 + r * t)
p is the principal
r is the interest rate per time period
t is the number of time periods
f is the future value
in this problem:
p = 10,000
r = 1.75% per year.
n = 39 weeks.
since one year is equal to 52 weeks, you can convert the number of weeks into years by dividing 39 by 52 to get .75 years.
since you want to know what is owed at the end of the time investment period, your formula would be:
f = p + p * r * t, which can also be shown as:
f = p * (1 + r * t).
when r is in years and t is in years, the formula becomes:
f = 10,000 * ( 1 + .0175 * .75) = 10,131.25
that's what is owed at the end of the 39 week period.
you can also work the problem in weeks.
to do that, you need the interest rate per week.
the interest rate per week is equal to .0175 per year divided by 52.
the formula becomes:
f = 10,000 * (1 + .0175/52 * 39) = 10,131.25
alternatively, you can just solve for the interest first and then add it to the principal.
the formula for interest is i = p * r * t.
this becomes:
i = 10,000 * .0175 * 39/52 = 131.25
add that to 10,000 to get 10,131.25.
in all of these formulas, the interest rate is used, not the percent.
rate = percent / 100.
1.75% is therefore equal to a rate of .0175.
the time periods must be consistent.
if the rate is per year, the number of time periods has to be in years.
if the number of time periods is in weeks, the rate must be per week.
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