question about math.of finance

1. Mr C wishes to withdraw savings from his RRSP. The government insists that banks withhold 10% of RRSP withdrawals as payment towards income taxes owing on the withdrawal. How much should Mr. C withdraw so as to have $1000 clear?

Amount clear = withdrawal amount x 90%
$1000 = withdrawal amount x 0.9
Withdrawal amount = $1000/0.9 = $1111.11

Mr. C withdraw should withdraw $1111.11 so as to have $1000 clear

Comment:
Mr. C can have his $1000 tax refund if his income falls below basic tax exemption amount in Canada or he still has to pay even more by April 30 if he is in high tax bracket. (more than 10% tax bracket)

2. A company borrowed $100000 on june 1, 2000, signing a promissory note at 12%
interest due in 90 days. On maturity, the company paid the accured interest and gave a second note for a further 90 day without interest and for an amount that when discounted at 13% on the day of issue, its proceeds were sufficient to pay the debt. Find: a) the amount of interest on the first note b) the face value of the second note

A important information is missing in this question. How frequent is interest compounded, daily, monthly, semi-annually or annually?
(a) It is assumed that interest is compounded annually at 12%
Interest = principal x interest rate (in decimal form) x term
Interest = $100000 x 0.12 x 90/365 = $2958.90

The amount of interest on the first note is $2958.90

(b) Amount = principal + principal x interest rate(in decimal) x term
principal{1 + interest rate(in decimal) x term}
$100000 = principal x (1 + 0.13 x 90/365)
$100000 = principal x 1.03205479
principal = $100000 / 1.03205479
principal = $96894.08

The face value of the second note is $96894.08

2011-05-25 20:24:27 補充：
Correction on comment:
Mr. C can have his $111.11 tax refund, (not $1000). $111.11 is what the bank withholds for income tax.