Question

You currently have $120,000 invested in shares and at the end of each year you save $8,000 from your wages to buy more shares, adding to your portfolio. If the shares' total expected return is 12% pa and all dividends are re-invested, calculate how many years it will take your share portfolio to reach $270,000. Round your answer up to the nearest year. Select one:

A. 4 years
B. 5 years
C. 6 years
D. 7 years
E. 8 years

Answer 1

Using the future value of a series formula for compound interest, it is calculated that the share portfolio will reach $270,000 after approximately 6 years. Therefore, rounded up to the nearest year, it would take 7 years.

Step-by-step explanation:

To calculate how many years it will take for the investment to grow to $270,000, we can use the future value of a series formula for compound interest. Specifically, we need to account for the additional $8,000 invested at the end of each year. The formula we use is:
FV = P × ((1 + r) n - 1) / r + PMT × (((1 + r) n - 1) / r) × (1 + r)

Where:

• FV stands for the future value of the investment.
• P is the present value of investment which is $120,000.
• r is the annual interest rate (12% or 0.12).
• PMT is the annual payment which is $8,000.
• n is the number of years.

Since we are solving for n, we would need to use a financial calculator or a similar tool because the equation cannot be rearranged algebraically to solve for n directly.

Using the inputs P = 120,000, r = 0.12, and PMT = 8,000, we iteratively test for n until FV exceeds $270,000. After computation, we find that the investment reaches slightly over $270,000 after 6 years, hence rounding up to the nearest year gives us 7 years.

Therefore, the answer is: D. 7 years.