# 200,000=R*[1-(1+0.025)^(-40)]/0.025) Solve for R?

200,000=R*[1-(1+0.025)^(-40)]/0.025)

Solve for R?

Relevance
• 4 years ago

200,000 = r * [1 - (1 + 0.025)^(-40) ] / 0.025

First, let's convert those decimals into fractions:

200,000 = r * [1 - (1 + 1/40)^(-40) ] / (1/40)

Division of fractions is the same as the multiplication of the reciprocal, so:

200,000 = r * [1 - (1 + 1/40)^(-40) ] * 40/1

200,000 = 40r * [1 - (1 + 1/40)^(-40) ]

Now let's divide both sides by 40:

5000 = r * [1 - (1 + 1/40)^(-40) ]

Now let's simplify the fraction sum in the center:

5000 = r * [1 - (40/40 + 1/40)^(-40) ]

5000 = r * [1 - (41/40)^(-40) ]

Next, let's resolve the negative exponent by finding the reciprocal:

5000 = r * [1 - (40/41)^(40) ]

We're going to have a 65 digit number if we actually determine 40^40, so at this point, I'll get a decimal approximation to 40/41, then use that to raise to the 40th power. While I'll be rounding writing numbers below, I won't be rounding in the calculator to limit rounding errors:

5000 ≈ r * (1 - 0.97561^40)

5000 ≈ r * (1 - 0.3724306)

5000 ≈ r * (0.6275694)

Now divide both sides by that decimal (remember, I still have the non-rounded value in my calculator, so you may get different results if you don't do the same):

r ≈ 5000 / 0.6275694

r ≈ 7967.24663 (rounded to 5DP)

• 4 years ago

DELETED QUESTION:

Determine f(-0.5) and f(1.5) from the following graph?

http://imgur.com/oHrdPtE

——————————————————————————————

Graph has vertex (1,4)

f(x) = a(x−1)² + 4

Graph passes through point (0,1)

1 = a(0−1)² + 4

1 = a + 4

a = −3

f(x) = −3(x−1)² + 4

f(−0.5) = −3(−0.5−1)² + 4 = −6.75 + 4 = −2.75

f(1.5) = −3(1.5−1)² + 4 = −0.75 + 4 = 3.25