In a Recent Flood Some Company Records Have Been Partially

In a recent flood some company records have been partially destroyed and it is your job to help reconstruct the missing data. For one of the company employees, Piper Jones, you have managed to gather some information regarding her pension. She currently earns $78,000 per year and expects to be paid through the company's defined benefits pension plan 7% of her final salary for each year of service. Given the state of the company, salaries are not expected to increase. You know that the pension payments should continue until her death, which actuaries expect to be when she turns 90 years old. You also know that the value of the future annuities at date of retirement should be $71,870 fulfill this commitment. Piper has just turn 55, however, you do not know her planned retirement age.
Required:
a. Determine Piper Jones planned retirement age assuming the company uses 5% interest rate for its pension plans.
b. Determine the current service cost for Piper Jones' pension for the past year (the year just before she turned 45).