✔ 最佳答案
The interest rate in a quarter is 7.5/4 = 1.875 %
Thererfore, at the end of first quarter, their renovations worth:
$5000 x 1.01875
Then they invest another $5000, summing up to:
$5000 x (1 + 1.01875)
At the end of second quarter, their renovations worth:
$5000 x (1 + 1.01875) x 1.01875
Then they invest another $5000, summing up to:
$5000 x (1 + 1.01875 + 1.018752)
So at the end of the n-th quarter, their renovations worth:
$5000 x (1 + 1.01875 + 1.018752 + 1.018753 + ... + 1.01875n-1) x 1.01875
= $5000 x 1.01875 x (1.01875n - 1)/(1.01875 - 1)
= $271667 x (1.01875n - 1)
For 5 years, there are 20 quarters and hence n = 20, giving the renovation worthing $271667 x (1.0187520 - 1) = $122236
So their targent cannot be met in 5 years.
2010-11-22 23:33:42 補充：
General formula:
1 + r + r^2 + r^3 + ... + r^n = [r^(n + 1) - 1]/(r - 1)
