Problem $5-14($Algo$)$ Deferred annuities; pension obligation $[$LO$5-8,5-10]$

Three employees of the Horizon Distributing Company will receive annual pension payments from the company when they retire. The employees will receive their annual payments for as long as they live. Life expectancy for each employee is $15$ years beyond retirement. Their names, the amount of their annual pension payments, and the date they will receive their first payment are shown below:

Employee Annual Payment Date of First Payment

Tinkers $ $26,00012/31/2027$

Evers $31,00012/31/2028$

Chance $36,00012/31/2029$

Required:

Compute the present value of the pension obligation to these three employees as of December $31,2024.$ Assume a $10\%$ interest rate.

The company wants to have enough cash invested at December $31,2027,$ to provide for all three employees. To accumulate enough cash, they will make three equal annual contributions to a fund that will earn $10\%$ interest compounded annually. The first contribution will be made on December $31,2024.$ Compute the amount of this required annual contribution.