Question

You have just accepted a job offer, which came with a signing bonus of $5,000 to be paid today in your retirement account. Your employer will also contribute an extra $10,000 at the end of each full year (you start work tomorrow!). If this account is expected to earn 10% p.a. compounded semi-annually, which number is closest to the amount of money will you have in that account after five years? (including the payment for that year). A) $59,500 B) $65,500 C) $69,500 D) $72,500 E) None of the above

Answer 1

Initial investment C= 5000

Rate of interest (r)= 10% annually, so semi annually, it will be = 10/2= 5%

Time = 5 and for compounding semi annually= 5*2= 10

Periodic payment P= 10000

For the initial bonus deposit,

FV= C* (1+r)ⁿ

= 5000(1+0.05)¹⁰

= 8144.48

Now, for the yearly deposits, the deposits are made annually and compounded semi-annually, so the formula cannot be used as it is for payments made in each compounding period and here payment is annual and compounding is semi annual, s the calculation will be done manual. The calculation is shown below:

Half years	Principal	interest	Amount due
end of 1st year	10,000.00	(10000*5%) 500	10000+500= 10500
half of 2nd year	10,500.00	(10500*5%) 525	10500+525= 11025
end of 2nd year	11025+10000= 21025	(21025*5%) 1051.25	22,076.25
half of 3rd year	22,076.25	1,103.81	23,180.06
end of 3rd year	23180+10000= 33180.06	1,659.00	34,839.07
half of 4th year	34,839.07	1,741.95	36,581.02
end of 4th year	36581+10000= 46581.02	2,329.05	48,910.07
half of 5th year	48,910.07	2,445.50	51,355.57
end of 5th year	51355+1000= 61355.57	-	61,355.57

First payment is done at the end of 1^st year, so the last payment will be at the end of 5^th year and so there will be no interest for the last payment made.

Now on every 6 month the interest is charged and the principal is updated to the amount due of the previous year.

And $10000 is added at the end of every year as given.

So as per the calculation above , the amount due to him after 5 years will be ,

$8144.47+ 61355.57

= $ 69,480.04

Or approximately $ 69,500.

so the answer is C.