F.1 maths

1.Mary deposits $6000 in a bank at an interest rate of R% p.a. If the interest rate changes to 5.5% p.a , Mary will get $180 more as the simple interest two years later. Find the value of R.

The interest will get from R% p.a after 2 years = 6000 * 2R% = 120R
The interest will get from 5.5% p.a after 2 years = 6000 * 2 * 5.5% = 660

Therefore,　660 - 120R = 180
　　　　　　　　　120R = 480
　　　　　　　　　　　R = 4

2.Susan deposits $7000 in a bank for 10 months. The bank pays simple interest at a certain interest rate per year. If Susan will get the amount of $7350 at the end of the period, what is the interest rate per year ?

Let r% be the interest rate.
Therefore,　7000 * [1+r%*(10/12)] = 7350
　　　　　　　　　 1+r% * (10/12) = 1.05
　　　　　　　　　　　　　　　r% = 0.05 * 12/10
　　　　　　　　　　　　　　　r% = 0.06　　(r = 6)
The interest rate per year is 6%


2007-02-11 16:35:20 補充：
3. Find the principal that will amount to $13156 after 73 days if simple interest is calculated at an interest rate of 6% p.a. ( take one year = 365 days ) Let P be the principal.So, P * [1 6% * (73/365)] = 13156　　P * [1 6% * 0.2] = 13156　　P * 1.012 = 13156　　　　　P = 13000

2007-02-11 16:38:40 補充：
4.Mimi desposits $13500 in Hang Fung Bank at an interest rate of 6.5% p.a. At the same time, this bank lends $150000 to Charles at an interest at an interest rate of 8.5%p.a.

2007-02-11 16:38:49 補充：
(a) Find the simple interest that Mimi will get after one year and Charles will pay after one year. Mimi will get after 1 year : 13500 * (1 6.5%) = $143775.5Charles will pay after one year : 150000 * (1 8.5%) = $162750

ANSER Q2:
THE INTEREST RATE PER YEAR IS:
(7350-7000)/10*12/7000*100%
=420/7000*100%
=6%
SO,THE INTEREST RATE PER YEAR IS 6%
(ANSWER Q2 ONLY)