Final answer:
The parents should place $1,071.84 at the end of each year into the savings account. They would earn $20,376.96 in interest over the life of the account. The value of the fund after 9 years would be $1,603.47. The interest earned during the 9th year would be $127.07.
Step-by-step explanation:
To calculate how much the parents should place at the end of each year into a savings account that earns an annual rate of 5.4% compounded annually, we can use the formula for the future value of an ordinary annuity:
Future Value = P * ((1 + r)^n - 1) / r
Where P is the annual payment, r is the annual interest rate, and n is the number of years. Plugging in the values from the question, we get:
32000 = P * ((1 + 0.054)^19 - 1) / 0.054
Solving for P, we find that the parents should place $1,071.84 at the end of each year into the savings account.
To determine the amount of interest earned over the life of the account, we can multiply the annual payment (P) by the number of years (19) and subtract the initial amount ($1,071.84 * 19 - $0). The interest earned over the life of the account would be $20,376.96.
To determine the value of the fund after 9 years, we can use the formula for the future value of a single sum:
Future Value = P * (1 + r)^n
Plugging in the values from the question, we get:
Future Value = $1,071.84 * (1 + 0.054)^9 = $1,603.47
To determine the interest earned during the 9th year, we can subtract the value of the fund after 8 years ($1,071.84 * (1 + 0.054)^8) from the value of the fund after 9 years ($1,071.84 * (1 + 0.054)^9).
Interest earned during the 9th year = $1,603.47 - $1,476.40 = $127.07