Question

Milo deposits $500 at the beginning of each year for 2 years into a fund that earns 8% annual effective. Half of the interest is reinvested at 10% annual effective and the remaining half is reinvested in Milo’s pocket (at 0%). Calculate the accumulated value in all three accounts in 10 years.

No excel solution please

Answer 1

Begining amount deposited to fund = $500

EAR = 8%

Interest rate at reinvested amount = 10%

Now, we have to calculate accumulated amount in 10 years in all the accounts.

End of the Year	Account 1 Accumulated Amount in fund	Account 2 Accumulated reinvested Interest @10%	Account 3 Accumulated amount in Milo's pocket @0%
1	$500 * (1+0.08) = $540	$0	$0
2	($500 + $500) * (1+0.08) = $1080	interest amount = 540 -500 = 40 Half of the interest = 40/2 = $20 invested at 10% $20 * (1+0.10) = $22	Second half of the interest amount = $20
3	( $1000 + $500 ) * (1.08) = $1620	($22 +$40) * (1.10) = $68.2	$20 + $40
4	($1500 + $500) * (1.08) = $2160	($68.2 + $60 ) *(1.10) = $141.02	$60 + $60 = $120
5	($2000 + $500) * (1.08) = $2700	($141.02 + $80) * (1.10) = $243.122	$120 +$80 = $200
6	($2500 + $500) * (1.08) = $3240	($243.122 + $100) * (1.10) = $377.4342	$220 + $100 = $320
7	($3000 + $500) * (1.08) = $3780	($377.4342 + $120) * (1.10) = $547.18	$340 + $120 = $460
8	($3500 + $500) * (1.08) = $4320	($547.18 + $140 ) * (1.10) = $755.90	$480 + $140 = $620
9	($4000 + $500) * (1.08) = $4860	($755.90 + $160) * (1.10) = $1007.50	$640 + $160 = $800
10	($4500 + $500) * (1.08) = $5400	($1007.50 + $180) * (1.10) = $1306.23	$820 + $180 = $1000

Interest calculation formula = Amount invested * ( 1 + effective rate)

Reinvested amount formula = (Amount accumulated at the end of the year - Amount invested in fund at the start of the year).

Hence, Accumulated amount at the end of the 10 year in three accounts are as follows:

Account 1 = $5400

Account 2 = $1306.23

and Account 3 = $1000