Question 1141590: A realtor borrowed $80,000 to develop some property. He was able to borrow part of the money at 3.5% interest and the rest at 5%. The annual interest on the two loans amounts to $3250. How much was borrowed at each rate? (Simple interest formula: I = P rt.)
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
(1) Using the standard algebraic approach....
Interest on amount x at 3.5% = (.035)(x)
Interest on amount (80000-x) at 5% = (.05)(80000-x)
Write and solve the equation that says the total interest is $3250.
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(2) A different method (much faster and easier, if you understand it)
$80000 at 3.5% = $2800
$80000 at 5% = $4000
Where the actual total interest of $3250 lies between $2800 and $4000 determines the ratio in which the loan is split between the two rates.
3250-2800 = 450; 4000-2800 = 1200; 450/1200 = 3/8
This means 3/8 of the $80,000 loan ($30,000) is at the higher rate.
ANSWER: $30,000 at 5%; $50,000 at 3.5%
CHECK: .05(30000) + .035(50000) = 1500+1750 = 3250
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