Eric borrowed a total of $4000 from two student loans. One loan charged 5% simple interest and the other charged 4.5% simple interest, both payable after graduation. If the interest he owed after 3 years was $547.50, determine the amount of principal for each loan.

Eric borrowed a total of $4000 from two student loans. One loan charged 5% simple interest and the other charged 4.5% simple interest, both payable after graduation. If the interest he owed after 3 years was $547.50, determine the amount of principal for each loan.

Question
Algebra foundations
asked 2020-10-28
Eric borrowed a total of $4000 from two student loans. One loan charged 5% simple interest and the other charged 4.5% simple interest, both payable after graduation. If the interest he owed after 3 years was $547.50, determine the amount of principal for each loan.

Answers (1)

2020-10-29
If x is invested at 5%, then 4000−x is invested at 4.5%.
The simple interest earned in 3 years is $547.50 so each year, the simple interest earned is $547.50/3=182.50 so we can write:
\(\displaystyle{0.05}{x}+{0.045}{\left({4000}−{x}\right)}={182.50}\)
Solve for x:
\(\displaystyle{0.05}{x}+{180}−{0.045}{x}={182.50}\)
\(\displaystyle{0.005}{x}={2.50}\)
\(\displaystyle{x}=\frac{{2.50}}{{0.005}}\)
\(\displaystyle{x}={500}\)
So, the Eric loaned $500 at 5% and $3,500 at 4.5%.
0

Relevant Questions

asked 2021-02-25
Laura borrowed a total of $18,000 from two different ba
to start a business. One bank charged the equivalent of 6% simple interest, and the other charged 7.5% interest. If the total interest after 2 years was $2220, determine the amount borrowed from each bank.
asked 2021-04-25
The unstable nucleus uranium-236 can be regarded as auniformly charged sphere of charge Q=+92e and radius \(\displaystyle{R}={7.4}\times{10}^{{-{15}}}\) m. In nuclear fission, this can divide into twosmaller nuclei, each of 1/2 the charge and 1/2 the voume of theoriginal uranium-236 nucleus. This is one of the reactionsthat occurred n the nuclear weapon that exploded over Hiroshima, Japan in August 1945.
A. Find the radii of the two "daughter" nuclei of charge+46e.
B. In a simple model for the fission process, immediatelyafter the uranium-236 nucleus has undergone fission the "daughter"nuclei are at rest and just touching. Calculate the kineticenergy that each of the "daughter" nuclei will have when they arevery far apart.
C. In this model the sum of the kinetic energies of the two"daughter" nuclei is the energy released by the fission of oneuranium-236 nucleus. Calculate the energy released by thefission of 10.0 kg of uranium-236. The atomic mass ofuranium-236 is 236 u, where 1 u = 1 atomic mass unit \(\displaystyle={1.66}\times{10}^{{-{27}}}\) kg. Express your answer both in joules and in kilotonsof TNT (1 kiloton of TNT releases 4.18 x 10^12 J when itexplodes).
asked 2021-03-05
Larry came up a little short one month at bill paying time and had to take out a title loan on his car at Check Casher's, Inc. He borrowed $260, and 3 weeks later he paid off the note for $297.50. What was the annual simple interest rate on this title loan?
asked 2021-05-11
Bethany needs to borrow \($10,000.\) She can borrow the money at \(5.5\%\) simple interest for 4 yr or she can borrow at \(5\%\) with interest compounded continuously for 4 yr.
a) How much total interest would Bethany pay at \(5.5\%\) simple interest?
b) How much total interest would Bethany pay at \(5%\) interest compounded continuously?
c) Which option results in less total interest?
asked 2021-03-26
A 1200kg pick up truck traveling south at 15m/s collides witha 750kg car traveling east. The two vehicles stick together. Thefinal position of the wreckage after the collision is 25m, atan angle of 50 south of east, from the point of impact. If thecoefficient of friction between the tires and the road, from thelocation of the collision to the point at which the wreckage comesto rest is 0.4, what was the speed of the car just before thecollision?
asked 2020-11-12
Finance bonds/dividends/loans exercises, need help or formulas
Some of the exercises, calculating the Ri is clear, but then i got stuck:
A security pays a yearly dividend of 7€ during 5 years, and on the 5th year we could sell it at a price of 75€, market rate is 19%, risk free rate 2%, beta 1,8. What would be its price today? 2.1 And if its dividend growths 1,7% each year along these 5 years-what would be its price?
A security pays a constant dividend of 0,90€ during 5 years and thereafter will be sold at 10 €, market rate 18%, risk free rate 2,5%, beta 1,55, what would be its price today?
At what price have i purchased a security if i already made a 5€ profit, and this security pays dividends as follows: first year 1,50 €, second year 2,25€, third year 3,10€ and on the 3d year i will sell it for 18€. Market rate is 8%, risk free rate 0,90%, beta=2,3.
What is the original maturity (in months) for a ZCB, face value 2500€, required rate of return 16% EAR if we paid 700€ and we bought it 6 month after the issuance, and actually we made an instant profit of 58,97€
You'll need 10 Vespas for your Parcel Delivery Business. Each Vespa has a price of 2850€ fully equipped. Your bank is going to fund this operation with a 5 year loan, 12% nominal rate at the beginning, and after increasing 1% every year. You'll have 5 years to fully amortize this loan. You want tot make monthly installments. At what price should you sell it after 3 1/2 years to lose only 10% of the remaining debt.
asked 2020-10-23
Chuck receives loans totaling $12,000 from two ba
. One bank charges 7.5% annual interest, and the second bank charges 6% annual interest. He paid $840 in total interest in one year. How much was loaned at each bank?
asked 2021-04-16
Two identical +9.5uC point charges are initially 3.5cm from eachother. If they are released att he same instant from rest, how fastwill each be moving when they are very far away from each other?Assume they have identical masses of 1.0mg.
asked 2021-01-13
Anonymous Anonymous Asked 10mths ago.
A college student earned $8900 during summer vacation working as a waiter in a popular restaurant. Part was invested at 10% simple interest and the remainder at 6% simple interest. At the end of one year, the student had earned $674 interest. How much was invested at 10%?
asked 2021-04-30
Two oppositely charged but otherwise identical conducting plates of area 2.50 square centimeters are separated by a dielectric 1.80 millimeters thick, with a dielectric constant of K=3.60. The resultant electric field in the dielectric is \(\displaystyle{1.20}\times{10}^{{6}}\) volts per meter.
Compute the magnitude of the charge per unit area \(\displaystyle\sigma\) on the conducting plate.
\(\displaystyle\sigma={\frac{{{c}}}{{{m}^{{2}}}}}\)
Compute the magnitude of the charge per unit area \(\displaystyle\sigma_{{1}}\) on the surfaces of the dielectric.
\(\displaystyle\sigma_{{1}}={\frac{{{c}}}{{{m}^{{2}}}}}\)
Find the total electric-field energy U stored in the capacitor.
u=J
...