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# interest earned

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?

This problem is the duplicate of her previous problem.

### 2 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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interest earned
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.
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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P( 1 + 0.06 ) ^ 5 =P( 1.28 )

P= 900/ 1.28 =703.12

Need to place \$703.12 , in 0.06 to grow to 900in 5 years.

P ( !+ 0.14) ^ 5 =P( 4. 49) = 900

P = 900/4.49 =200.44

at Compound interest rate of 14% , only need to invest \$200 to grow to 900 in 5 years.

At 6% rate investment should be