you are offered $900 five years from now or $150 at the end of each year for the next five years. If you can earn 6 percent on your funds, which offer will you accept? If you can earn 14 percent on your funds, which offer will you accept? why are your answers different?

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you are offered $900 five years from now or $150 at the end of each year for the next five years. If you can earn 6 percent on your funds, which offer will you accept? If you can earn 14 percent on your funds, which offer will you accept? why are your answers different?

3 hours ago | Amy from Slippery Rock, PA | 1 Answer | 0 Votes

A = 150 + 150(1+r) + 150(1+r)^2 + 150(1+r)^3 + 150(1+r)^4

(1+r)A = 150(1+r) + 150(1+r)^2 + 150(1+r)^3 + 150(1+r)^4 + 150(1+r)^5

A - (1+r)A = 150 - 150(1+r)^5

A = 150 (1 - (1+r)^5) / (1 - 1 - r)

A = 150 ( (1+r)^5 - 1) / r

[N.B.: A is a geometric series. The formula for the first n terms is sum{1,n}(a*(k^n - 1)/(k - 1)). For A, a =150, k = (1+r), and n = 5. But every student should know how to derive that formula; which is essentially what I did.]

For what r is A > 900?

150 ( (1+r)^5 - 1) / r > 900

( (1+r)^5 - 1) / r > 6

(1+r)^5 > 6 r + 1

---check for r = 6%:

(1.06)^5 >? 6(0.06) + 1

1.3382255776 >? 1.36

No.

So 6% would not give you more than $900 in 5 years.

---check for r = 14%:

(1.14)^5 >? 6(0.14) + 1

1.925414582400001 >? 1.84

Yes.

So 14% would give you more than $900 in 5 years.

you are offered $900 five years from now or $150 at the end of each year for the next five years. If you can earn 6 percent on your funds, which offer will you accept? If you can earn 14 percent on your funds, which offer will you accept? why are your answers different?

3 hours ago | Amy from Slippery Rock, PA | 1 Answer | 0 Votes

A = 150 + 150(1+r) + 150(1+r)^2 + 150(1+r)^3 + 150(1+r)^4

(1+r)A = 150(1+r) + 150(1+r)^2 + 150(1+r)^3 + 150(1+r)^4 + 150(1+r)^5

A - (1+r)A = 150 - 150(1+r)^5

A = 150 (1 - (1+r)^5) / (1 - 1 - r)

A = 150 ( (1+r)^5 - 1) / r

[N.B.: A is a geometric series. The formula for the first n terms is sum{1,n}(a*(k^n - 1)/(k - 1)). For A, a =150, k = (1+r), and n = 5. But every student should know how to derive that formula; which is essentially what I did.]

For what r is A > 900?

150 ( (1+r)^5 - 1) / r > 900

( (1+r)^5 - 1) / r > 6

(1+r)^5 > 6 r + 1

---check for r = 6%:

(1.06)^5 >? 6(0.06) + 1

1.3382255776 >? 1.36

No.

So 6% would not give you more than $900 in 5 years.

---check for r = 14%:

(1.14)^5 >? 6(0.14) + 1

1.925414582400001 >? 1.84

Yes.

So 14% would give you more than $900 in 5 years.

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