Question

# Derek currently has \$13,772.00 in an account that pays 6.00%. He will withdraw \$5,561.00 every other...

Derek currently has \$13,772.00 in an account that pays 6.00%. He will withdraw \$5,561.00 every other year beginning next year until he has taken 6.00 withdrawals. He will deposit \$13772.0 every other year beginning two years from today until he has made 6.0 deposits. How much will be in the account 27.00 years from today? Answer format: Round to 2 decimal places

Present value of withdrawals=Cash withdrawals*Present value of discounting factor(rate%,time period)

=5,561/1.06+5,561/1.06^2+5,561/1.06^3+5,561/1.06^4+5,561/1.06^5+5,561/1.06^6

=27345.2406

Present value of deposits=Cash deposits*Present value of discounting factor(rate%,time period)

=13772/1.06^2+13772/1.06^3+13772/1.06^4+13772/1.06^5+13772/1.06^6+13772/1.06^7

=63888.1044

Hence total present value=13,772-27345.2406+63888.1044

=\$50314.8638

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period

A=50314.8638*(1.06)^27

=\$242635.68(Approx)

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