Use the formula for the present value of an ordinary annuity or the amortization formula to solve the following problem.
pv=$15,000; i=0.03; pmt=$650; n=?
n= (round up to the nearest integer.)
use the formula for the present value of an ordinary annuity or the amortization formula to solve the following problem.
pv=$9,000; pmt=$500; n=35; i=?
i= (type an integer or decimal rounded to three decimal places as needed.)

  1.  n = 40

  2.  

Step-by-step explanation:

The ordinary annuity formula can be written as ...

  PV = PMT(1 -(1+r)^-n)/r

where PMT is the payment per period, r is the interest rate per period, and n is the number of periods.

This formula can be solved explicitly for n, but not for r. Iterative or other methods can be used to find r.

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1. Filling in the given information, we have ...

  15000 = 650(1 -1.03^-n)/0.03

  450/650 = 1 - 1.03^-n . . . . . divide by the coefficient of the stuff in parens

  1.03^-n = 4/13 . . . . . . . . . . . solve for the exponential term

  -n·log(1.03) = log(4/13) . . . . take logarithms

  n = log(13/4)/log(1.03) ≈ 39.87 . . . . . solve for n

  n ≈ 40

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2. We can rewrite the annuity formula to make it be a function of i that is zero at the desired value of i.

  f(i) = PV -PMT(1 -(1+i)^-n)/i

If we want i as a percentage, then we can replace i with i/100 and fill in the given values to get ...

  f(i) = 9000 -500(1 -(1 +i/100)^-35)/(i/100)

  f(i) = 1000(9 -50(1 -(1 +i/100)^-35)/i) . . . . multiply the fraction by 100/100

Since we're seeking a value of f(r) that is zero, we can eliminate the factor of 1000.

  f(i) = 9 -50(1 - (1+i/100)^-35)/i

The attached graph shows the solution to f(i)=0 is near i=4.27%. As a decimal rounded to 3 decimal places, this is ...

  i ≈ 0.043

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

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step-by-step explanation:

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