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g You want to save sufficient funds to generate an annual cash flow of $50,000 a year for 20 years as retirement income. You currently have no retirement savings but plan to save an equal amount each year for the next 30 years until your retirement. How much do you need to save each year if you can earn 8 percent on the savings? (10 Points)

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truonghanhduyen

Answer:

You need to save $4,012.45 each year

Explanation:

Pertiuty in 20 years  is $50,000.

So the amount must be in account after 30 years saving to enough for above pertiuty is calculated as below:

= $50000/(1+8%)+ $50000/(1+8%)^2+......+$50000/(1+8%)^20

= $50,000 * Annuity Factor ( 1-20 years) of 8%

=$50000*9.818

= $490,907

To have $490,907 (FV) in account after 30 years (tenor), now you have save an amount each year (PMT) calculated as below:

$490,907 = PMT*(1+8%)^30+....PMT*(1+8%)^2 + PMT*(1+8%)

= PMT * Discount Factor ( 1-30 years) of 8%

$490,907 = PMT * 122.346

-> PMT = $490,907/ 122.346

= $4,012.45

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