Question

you invest $10,000 with your cousins successful Alpha Fund. Even though you withdraw $1,000 at the end of the next 3 years, you are able to quadruple you investment in 3 years. Approximately what interest rate did you earn?

a. 30%

b. 45%

c. 66%

d. 18%

e. 52%

f. 34%

Answer 1

The question hasn't specified if $1000 withdrawal is made at the end of each of three years OR at the end of the third year.So I have worked out both ways.

Alternative 1 $1000 withdrawal is made at the end of each of three years

Let Amount at the end of year 1 be x

x = 10000 (1 + r)

x = 10000 + 10000r - (1)

Let Amount at the end of year 2 be y

y = ( x - 1000) (1+r)   

Substituting for x

y = (10000 + 10000r-1000) (1+r)  

= (9000 + 10000r)(1+r)

= 9000 + 10000r +9000r + 10000r²

= 9000 + 19000r + 10000r²   - (2)

For year 3

41000 = y - 1000 (1+ r )

Substituting for y

41000 = (9000 + 19000r + 10000r² - 1000) (1+ r )

41000 = (8000 + 19000r + 10000r² ) (1+ r )

41000 = 8000 + 19000r + 10000r² + 8000r + 19000r² + 10000r³

33000 =27000r + 29000r² + 10000r³

Since it is a multiple choice I have substituted r directly with the answers ( Hint : since the amount quadrupled the interest rate is likely to be high)

Substituting with 66%

27000 * 0.66 + 29000 * 0.66 * 0.66 + 10000* 0.66 * 0.66 * 0.66

=33,327 Which is near to 33000.

Ans: (B) 66%

Alternative 2: $1000 withdrawal is made at the end of three years

Given that the investment is quadrupled even after $ 1000 is removed at the end of the next three years. So the Amount is $1000+ (10000 * 4 ) = 41,000 at the end of the third year.

41000 = 10000 ( 1 + r )³

4.1 = ( 1 + r )³

3√4.1 = ( 1 + r )

1.6005 - 1 = r

60% = r