Mr. Jones intends to retire in 20 years at the age of 65. As yet he has not prov

Question

Mr. Jones intends to retire in 20 years at the age of 65. As yet he has not provided for retirement income, and he wants to set up a periodic savings plan to do this. If he makes equal annual payments into a savings account that pays 4 percent interest per year, how large must his payments be to ensure that after retirement he will be able to draw $30,000 per year from this account until he is 80?

Here is what I'm thinking the answer is:
He is 45 yrs. Old, wants to retire in 20 years. He wants to draw 30k/year for 15 years.
To draw that amount, he needs a total of 450,000
4% interest on 450,000 = 18,000
450,000 – 18,000 = 432,000/20years = 21,600 savings per year

Am I on the right track?

Explanation / Answer

Present value PV= C{1-[1/(1+r)t]}/r 30,000{1-[1/(1+0.04)15]}/0.04 30,000(11.125) 333,552 Future Value FV= C[(1+r)t-1]/r 333,552= C[(1+0.04)20-1]/0.04 C[1.1911]/0.04 C(29.777) C= 333,552/29.777 C= 11,201.66 Savings per year = $11,201.66

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