Anne is planning to attend college when she graduates from high school in 7 years from now. She anticipates that she will need $10,000 at the beginning of each college year to pay for tuition and fees, and have some spending money.
Anne has made an arrangement with her father to do chores if her dad deposits $3,500 at the end of each year for the next 7 years in a bank account paying 8% interest. Will there be enough money in the account for Anne to pay for her college expenses? Assume the rate of interest stays at 8 percent during the college year.
She needs $10,000 in 7 years, making $3,500 each year, with 08% interest.
Starting: $0.00
After the first year: $3,500
After the second year: ($3,500 (.08)) + $3,500 + $3,500 = 7,280
After the third year (7,280 (.08)) + $3,500 + $7,280 = 11,082.40
She has enough for a year. Basically, find the interest on the last year and then add the newest amount of money to the last year's return.
What major benefits do corporations and investors enjoy because of the existence of organized
security exchanges?
To determine whether there will be enough money in the account for Anne to pay for her college expenses, we need to calculate the future value of her father's deposits with interest.
The formula to calculate the future value of an account with compound interest is:
FV = P(1 + r/n)^(n*t)
Where:
FV is the future value
P is the principal (initial deposit)
r is the annual interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, the principal (P) is $3,500, the annual interest rate (r) is 8% (or 0.08 as a decimal), the number of times interest is compounded per year (n) is 1, and the number of years (t) is 7.
Using the formula:
FV = $3,500 * (1 + 0.08/1)^(1*7)
FV = $3,500 * (1.08)^7
Now, we can calculate the future value of the annual deposits:
FV = $3,500 * 1.717095
FV = $5,999.33
Therefore, there will not be enough money in the account for Anne to pay for her college expenses.