# S3 math!!!

(1)a new car is worth \$250 000 and its depreciation rate is 30% for the first year and 20% for every subsequent year

(a) find its value 3 years later

(b) find the overall percentage change in its value over these 3 years

(2) jack deposits \$80 000 in a bank at 6% p.a. for 2 year. find the mount obtained if the interest is compounded

(a) quarterly

(b) monthly

(2) jack deposits \$80 000 in a bank at 6% p.a. for 1 year. find the amount obtained if the interest is compounded

(a) quarterly

(b) monthly

### 2 個解答

Lv 7
8 年前
最愛解答

(1)

(a)

The value of the car 3 years later

= \$250 000 x (1 - 30%) x (1 - 20%)²

= \$112 000

(b)

Overall percentage change

= [(112 000 - 250 000)/250 000] x 100%

= -55.2%

(decrease 55.2%)

=====

(2)

(a)

Principal, P = \$80 000

Interest rate, R% = 6%/4 = 1.5%

No. of periods, n = 2 x 4 = 8

Amount, A

= P (1 + R%)^n

= \$80 000 x (1 + 1.5%)^8

= \$90 119.41 (to 2 decimal places)

(b)

Principal, P = \$80 000

Interest rate, R% = 6%/12 = 0.5%

No. of periods, n = 2 x 12 = 24

Amount, A

= P (1 + R%)^n

= \$80 000 x (1 + 0.5%)^24

= \$90 172.78 (to 2 decimal places)

2012-12-26 22:48:44 補充：

(2)(a)

Amount, A = \$90 119 (to the nearest dollar)

(2)(b)

Amount, A = \$90 173 (to the nearest dollar)

2012-12-26 22:55:40 補充：

(2)

If it is 1 year instead of 2 years, the solutions are :

(a)

Principal, P = \$80 000

Interest rate, R% = 6%/4 = 1.5%

No. of periods, n = 4

Amount, A

= P (1 + R%)^n

= \$80 000 x (1 + 1.5%)^4

= \$84 909 (to the nearest dollar) ...... ans

2012-12-26 22:55:52 補充：

(b)

Principal, P = \$80 000

Interest rate, R% = 6%/12 = 0.5%

No. of periods, n = 12

Amount, A

= P (1 + R%)^n

= \$80 000 x (1 + 0.5%)^12

= \$84 934 (to the nearest dollar) ...... ans

• 8 年前

1a)

Its value

=250,000(1-30%)(1-20%)^2

=\$112,000

1b)

The change

=(112,000-250,000)/250,000 x 100%

= -55.2%

Thus, the value decreased by 55.2%

2a)

Amount

=80,000[1+(6%/4)]^4

=\$84,909, corr to the nearest \$1

2b)

Amount

=80,000[1+(6%/12)]^12

=\$84,934, corr. to the nearest \$1