A.) You are planning to save for retirement over the next 15 years. To do this,

Question

A.)

You are planning to save for retirement over the next 15 years. To do this, you will invest $650 per month into a stock account that will provide a 10% annual return. In addition, your employer has agreed to make 240 monthly payments of $200 each into a trust account to fund your retirement which will provide a 7% annual return. All payments will be made at the end of each month. At the end of 15 years, you will be paid 10 equal annual payments with the first payment being made at the beginning of year 16. The funds will be invested at a nominal rate of 5% with monthly compounding during the distribution period. How large will each of your 10 retirement period payments be?

B.)

If you invest a lump sum of $5,000 dollars of your own money now to supplement your stock account (same investment fund), how much will your annual payments be during your retirement years?  

Explanation / Answer

The value of $650 per ,onth for 15 years (180 months) will be = fv(rate,nper,pmt) where rate = 0.10/12, nper =180 and pmt =650.

The future value of $650 for 15 years =fv(0.10/12,180,650) = 269,405.73

The future value of $200 for 15 years in turst account at 7% =fv(0.07/12,180,200) = 63,392.46

The total retirement corpus will be 269,405.73 +  63,392.46 = 332,798.18

Now with this as the pv , we will calculate the value of the the 10 year retirement payment =pmt(rate,nper,pv)

The rate of 5% with monthly compounding =(1+0.05/12)^12 - 1

The 10 year retirement payment =pmt((1+0.05/12)^12-1,10,332798.18) = 43,342.41

Each of your 10 retirement period payments be =$43,342.41

(b) Retirement corpus will be with 5000 lumpsum =332,798.18 +fv(0.10,15,0,5000) = 332,798.18 + 20,886.24 = 353,684.43

The 10 year retirement payment =pmt((1+0.05/12)^12-1,10,353684.43) = 46,062.56

Each of your 10 retirement period payments be =$46,062.56

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.