SOLUTION: I am having trouble setting up these problems, I do not know which formula to use r=I/pt or I=Prt An investor earned $1080 on an investment of $60,000 in 45 days. Find the ann

Question 844305: I am having trouble setting up these problems, I do not know which formula to use r=I/pt or I=Prt

An investor earned $1080 on an investment of $60,000 in 45 days. Find the annual simple interest rate earned on the investment.
Capitol City Bank approves a home-improvement loan application for $17,000 at an annual simple interest rate of 9.75% for 270 days. What is the maturity value of the loan?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
I'm assuming a year is equal to 365 days.
If the number of days per year you are using is different than this, you will need to re-calculate using your number of days per year instead.

I'm assuming T will be measured in years, so 45 days is equal to 45 / 365 years.

Likewise 270 days will be equal to 270 / 365 years.

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An investor earned $1080 on an investment of $60,000 in 45 days. Find the annual simple interest rate earned on the investment.

use I = PRT.

I = 1080
P = 60000
R = interest rate per year you are looking for.
T = 45 / 365 years

Formula becomes:

1080 = 60000 * R * 45/365

divide both sides of this equation by 60000 and multiply both sides of this equation by 365/45 to get:
1080 / 60000 * 365/45 = R
solve for R to get:
R = .146 which is equal to 14.6% per year simple interest.

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Capitol City Bank approves a home-improvement loan application for $17,000 at an annual simple interest rate of 9.75% for 270 days. What is the maturity value of the loan?

You are now looking for the maturity value of the loan which is the same as the future value of the loan.

The future value of the loan is the principal plus the interest, not just the interest.

the formula for simple interest is equal to I = PRT.
the formula for future value of the loan is F = P + I, where P is the principal and I is the interest.
since I = PRT, this formula can also be shown as F = P + PRT.
you can also factor out the common P to get F = P * (1 + RT).

in this problem:
P = 17000
R = .0975 per year
T = 270 / 365 years

the formula we'll use is F = P + PRT.
this formula becomes:
F = 17000 + 17000*.0975*270/365
solve for F to get:
F = 17000 + 1226.10 which results in:
F = 18226.10

The maturity value of the loan is equal to $18,226.10.

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