F.3 MATHS(PERCENTAGE)5点

2011-09-27 5:07 am

1. Grace borrowed $42000 from a bank for 5 years to buy a new car.
The interest was compounded quarterly.
a) If the amount she has to repay after 3 months is $42630, find the annual interest rate of her loan.
b) Find the compound interest the bank will earn after 5 years.

2. The interest rate provided by bank A is 3.5%, compounded yearly. The interest rate provided by bank b is3.2%, compounded half- yearly. Find the difference in the amount of interest earned if $55000 is deposited in both accounts for 4 years.

i wanna know the steps

ANs: 1a) 6%
b) $14567.91
2. $666.65

回答 (1)

Kelvin

2011-09-27 5:23 am

✔ 最佳答案

1. let x be the annual interest rate
42000 x ( 1+ x/4) = 42630
1+ x/4 = 1.015
x/4 = 0.15
x = 0.06 = 6%

1b. the bank will earn :
42000 x (1 + 6%/4) ^ 20 - 42000
= 42000 x 1.347 - 42000
= 14567.91

2. compounded yearly:
55000 x (1+3.5%) ^ 4 = 63113.77
compounded half-yearly
55000 x (1+3.2%/2) ^ 8 = 62447.11

different = 63113.77 - 62447.11 = 666.65

Q1a 睇返書
1b 年利率 6% 每1/4 年既息 = 6% / 4 = 1.5%
五年派二十次息 (一年四次派五年)
所以係二十次方，減返個本就係銀行賺既

2. 因為每半年派一次，所以每半年既利率 = 3.2% / 2 = 1.6%
四次派八次息，所以八次方

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