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Gennadij [26K]
3 years ago
7

After 8 years a loan grows to $75 210. If the interest was compounded annually at a rate of 8.5%, find the size of the initial l

oan to the nearest dollar.
Mathematics
1 answer:
stealth61 [152]3 years ago
3 0
Given:
Future Value = $75,210
term = 8 years
rate = 8.5%
Initial loan = ?

In this case, we need to find the present value of the loan. Compounded means that even the interest has an interest.

PV = FV / (1 + i)^n

PV = 75,210 / (1 + 0.085)⁸

PV = 75,210 / (1.085)⁸

PV = 75,210 / 1.9206

PV = 39,159.64

Initial loan is $39,159.64
total interest is $75,210 - 39,159.64 = $36,050.36

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Slope-intercept form: y=mx+b where <em>m</em> is the slope and <em>b</em> is the y-intercept (the value of y when x=0)

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How many lb of brand X sugar which
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Answer:  <u>4 pounds</u> of brand X sugar

====================================================

Reason:

n = number of pounds of brand X sugar

5n = cost of buying those n pounds, at $5 per pound

Brand Y costs $2 per pound, and you buy 8 lbs of it, so that's another 2*8 = 16 dollars.

5n+16 = total cost of brand X and brand Y combined

n+8 = total amount of sugar bought, in pounds

3(n+8) = total cost because we buy n+8 pounds at $3 per pound

The 5n+16 and 3(n+8) represent the same total cost.

Set them equal to each other. Solve for n.

5n+16 = 3(n+8)

5n+16 = 3n+24

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-------------

Check:

n = 4

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The answer is confirmed.

--------------

Another way to verify:

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5*4+16 = 3(4+8)

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36 = 36

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