復合利率,等差 數學問題

1.Mr. Jameson deposits $7000 into a high-risk fund at the end of each
year for 10 years. If the growth rate is 10% per annum, how much will
the high-risk fund be at the end of 10 years? (correct to nearest
dollars)
The amount of the high-risk fund be at the end of 10 years
= 7000(1+10%)^(10) + 7000(1+10%)^9 + ... + 7000
= 7000[(1+10%)^7 - 1]/(1+10%-1)
= $66410 (corr to nearest $1)

2.In a sales promotion, a supermarket supervisor orders Jimmy to display
XYZ coffee by piling them up in n layers in front of show window, and
the number forms an arithmetic sequence. The top, second and bottom
layers have 1, 4 and 16 packs of coffee respectively. Find the number of
layers n.
a = 1, d = 4-1 = 3
a + (n-1)d = 16
1 + (n-1)3 = 16
3n-3 = 15
3n=18
n = 6
The number of
layers is 6.

3.The sale of a XBox software was 4500 sets in April. The sale is
increased by the same quantity d sets each month. If the sale in
December was 6900 sets, find the value of d.
a = 4500, a + (n-1)d = 6900, n = 12-4 = 8
4500 + (8-1)d = 6900
7d = 2400
d = 342.9 (corr to 1 d.p.)

4.Tommy’s annual income is $120,000. At the beginning of every year,
Tommy deposits one-tenth of his income in ABC Bank at an interest rate
of 5% p.a. compounded yearly. Find the total amount accumulated at the
end of the fourth year. (correct to nearest dollars)
The total amount accumulated at the
end of the fourth year
= (120000/10)(1+5%)^4 + (120000/10)(1+5%)^3 + ... + (120000/10)(1+5%)+120000/10
= (12000)[(1+5%)^4 - 1]/(1+5%-1)
= $51721.5

5.Find the smallest term of the A.P. 5, 12, 19, … which is greater than
1000.
a = 5, d = 12-5 = 19-12 = 7,
a + (n-1)d > 1000
5 + 7(n-1) > 1000
7n-7 = >995
7n > 1002
n > 143 (corr to nearest integer)
The smallest term is the 144 th term.
and it is = 5+7(144-1)=1006