Question

The Power of Long-Term Compounding The average long-term stock market return: adjusted for inflation, is about 7 per year. Two workers invest in a mutual fund (an account that includes shares of many different stocks) and their earnings per year follow this typical 7% growth rate. (w) Angelastarteds depositing $1000 per year into the fund at age 25. She does this for 10 years, but then she has to stop due to other factors in her life She lets that money sit in the fund for 40 years, until she is 75 a) What is her balance at that point? b) How much did she deposit into the account?

Answer 1

a) At age 75, Angela's balance in the mutual fund is approximately $305,717.69.

b) Over the 10 years of deposits, Angela contributed a total of $10,000 to the account.

Step-by-step explanation:

To calculate Angela's balance at age 75, we can use the future value of an annuity formula:

`\[ FV = P \left( ((1 + r)^(nt) - 1)/(r) \right) \]`

where P is the annual deposit, r is the annual interest rate (expressed as a decimal), n is the number of compounding periods per year, and t is the number of years. In Angela's case, she deposited $1000 annually for 10 years, and then the money was left to grow for an additional 40 years at an average annual interest rate of 7%.

Plugging in the values, we get:

`\[ FV = 1000 \left( ((1 + 0.07)^(1 * 50) - 1)/(0.07) \right) \]`

Calculating this expression results in Angela's balance at age 75, which is approximately $305,717.69.

To determine the total amount deposited into the account, we simply multiply Angela's annual deposit by the number of years she contributed:

`\[ \text{Total Deposit} = 1000 * 10 = 10,000 \]`

Therefore, Angela contributed a total of $10,000 to the mutual fund over the 10-year period. Understanding the power of long-term compounding illustrates the potential for wealth accumulation through consistent and disciplined investing, even with a limited initial investment.