Question

Your broker correctly tells you that your portfolio's average annual rate of return for the past two years is 10.0%. You know the portfolio value today of

$34,300 is $1,700 less than when you started the account two years ago. What was the portfolio's value one year ago?

a. $23,476       b. 828,406       c. $31,247       d. $25,824       e. $21,342

MUST USE TIME VALUE OF MONEY FORMULAS OR "BA II PLUS CALCULATOR" IN ORDER TO SOLVE / EXCEL NOT ALLOWED

Answer 1

You know the portfolio value today of $34,300 is $1,700 less than when you started the account two years ago; therefore the portfolio value two years ago was= $34,300 + $1,700 = $36,000

Assume that the portfolio value one year ago was X

As your broker correctly tells you that your portfolio's average annual rate of return for the past two years is 10.0% therefore sum of annual rate of return for the past two years is 20% or we can write an equation in following manner

Annual return of year one + annual return of year 2 = 20%

Or (X - $36,000)/$36,000 + ($34,300 –X)/X = 20%

Or (X/$36,000) – 1 + ($34,300/X) – 1 = 20%

Or (X/$36,000) + ($34,300/X) = 20% +2 = 2.20

Or (X^2 + $34,300 * $36,000)/$36,000*X = 2.20

Or X^2 + $1,234,800,000 = 2.20 * $36,000 * X

Or X^2 + $1,234,800,000 = $79,200 * X

Or $1,234,800,000 = $79,200 * X – X^2

After solving the equation we get (we can put different values of given options and check for the right value which satisfies the equation)

X = $21,342

Therefore correct answer is option e. $21,342