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

2.

A savings account was established with $36,000 exactly 7 years ago. The account earns 4.3% compounded annually. Otherwise, the account has been left alone. When the annual interest is credited to the account today, how much interest is credited?

a. $2,918       b. $2,411       c. $ 1,993      d. $2,652       e. $2,192

3.

A savings account was established with $36,000 exactly 7 years ago. The account earns 4.3% compounded annually. Otherwise, the account has been left alone. Next year, how much interest-on-interest will the account earn?

a. $482       b. $438       c. $584       d. $642       e. $531

Answer 1

1. 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?

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 = $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 as follows

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

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

2. A savings account was established with $36,000 exactly 7 years ago. The account earns 4.3% compounded annually. Otherwise, the account has been left alone. When the annual interest is credited to the account today, how much interest is credited?

Let’s calculate the portfolio value after 6 years as the annual interest is credited to the account today (after 7 years) in the interest on the portfolio value after 6 years

The portfolio value after 6 years = Initial investment * (1+ r) ^t

Where,

Initial investment 7 years ago was $36,000

r is the annual interest rate = 4.3%

t is the time period = 6 years

Therefore,

The portfolio value after 6 years = $36,000 * (1+ 4.3%) ^6

= $46,345.58

Now the annual interest is credited to the account today (after 7 years)

= Interest on the portfolio value after 6 years

= 4.3% * $46,345.58

= $1992.86 or $1,993

Therefore correct answer is option c. $1,993

3. A savings account was established with $36,000 exactly 7 years ago. The account earns 4.3% compounded annually. Otherwise, the account has been left alone. Next year, how much interest-on-interest will the account earn?

Next year (after 8 years) the interest-on-interest the account will earn = Interest earned up to year 7 * 4.3%

Now we have to calculate interest earned up to year 7 = Initial investment * (1+ r) ^t - Initial investment

Where,

Initial investment 7 years ago was $36,000

r is the annual interest rate = 4.3%

t is the time period = 7 years

Interest earned up to year 7 = $36,000 * (1+ 4.3%) ^7 - $36,000

= $48,338.44 - $36,000

= $12,338.44

Next year (after 8 years) the interest-on-interest the account will earn = $12,338.44 * 4.3%

= $530.55 or $531

Therefore correct answer is option e. $531