Question

William receives an inheritance of $100,000. he invests the lump sum at a rate of interest of 8% compounded quarterly. 2 years later he begins to deposit $3000 at the end of every 6 months and earns 9% compounded semi-annually. what is the value of williams investments after 8 years from the original investment?

Answer 1

The value of William's investments after 8 years from the original investment is $221,938.90. After 8 years, William's investments, comprising an initial $100,000 and regular $3,000 deposits, would accumulate to approximately $221,938.90.

Step-by-step explanation:

To calculate the value of William's investments after 8 years, we need to calculate the future value of his initial investment and the future value of his deposits. First, let's calculate the future value of the initial investment:

Future Value = Principal * (1 + (Rate/Compounding Frequency))^(Compounding Frequency * Time)

Future Value = $100,000 * (1 + (0.08/4))^(4 * 2) = $100,000 * (1 + 0.02)^8 = $100,000 * (1.02)^8 = $116,243.08

Now, let's calculate the future value of the deposits:

Future Value = Deposit * ((1 + (Rate/Compounding Frequency))^(Compounding Frequency * Time) - 1) / (Rate/Compounding Frequency)

Future Value = $3,000 * ((1 + (0.09/2))^(2 * 16) - 1) / (0.09/2) = $3,000 * (1.045)^32 * (1.045 - 1) / 0.045 = $3,000 * (1.045^32 - 1) / 0.045 = $105,695.82

Finally, the total value of William's investments after 8 years is the sum of the future value of the initial investment and the future value of the deposits: $116,243.08 + $105,695.82 = $221,938.90