Question

2. Mike currently 48, has $20,000 saved for retirement. He is currently saving $500 at the beginning of every month and his employer matches his total savings contribution on a monthly basis. Mike projects that he could earn 9% on his savings. He plans to retire at 65 and expects to live until age 85. His current expenditure on basic needs at the beginning of every month is $2500 every month which is expected to increase with inflation of 3%.

(a) What would be the value of Mike’s savings (including employer’s contribution) at the age of 65?

here is the answer but can you explained why in part A my professor multiple PMT of 500 by 2

solution

1. Use BGN mode:
   N=65-48=17 years = 204 months I/Y= 9/12=0.75
   PV=20000
   PMT=2*500=1000
   FV=? 574,347.88

Answer 1

Answer:

Explanation of why professor has used 500 multiply by 2 as PMT.

The question says:

"He is currently saving $500 at the beginning of every month and his employer matches his total savings contribution on a monthly basis."

So Mike saves $500 and his employer also contributes equal amount of $500 on a monthly basis.

As such monthly saving = $500 * 2

Hence:

PMT = $500 * 2

N = 17 * 12 = 204 months

Interest rate = I/ Y = 9/12 = 0.75

PV=20000

FV = FV(rate, nper, pmt, pv, type) = FV (0.75%, 204, -1000, -20000, 1) = $574,347.88

Hope this clarifies.