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Mrs. Anna: She has just turned 52 years. Therefore, she still has 13 years to her retirement age of 65 years. Anna has 850,000 in has savings account. She is contemplating with the option of placing $500,000 in her fixed account rather than to use the pension scheme.
IKAO Social Security Fund: It will provide an annuity of $25,000 for 15 years when she retires at the age of 65. The company will fund this plan, which will have an annuity-due of 15 years. The company will pay an interest of 6.5%. The company will be demanding for an installment of $12,000 per annum.
Present Value of Retirement Annuity PVA= A[((1-(1.065)-15)/0.065]
PVA= 25,000[((1-(1.065)-15)/0.065]
PVA= 235,066.72
The equivalent amount of present value instalment that the company should be issuing
(1.065)13– 1)/(1-(1.065)-1 = 1.26749/0.06103286= 20.767295
Therefore,
P= 235066.72/= 20.767295=11,319.08
Difference between instalment and price
12,000-11,319.08= 680.92
Additional monthly fee= 680.92/12= 56.67