# MATHS: interest

Mary has found her dream house. It is selling for \$500000. When she retires 2 years from now, she plans to sell her present house for \$450000 an move. She decides to set aside \$900 every two weeks until she retires in a fund earning 10.5%/a, compounded every second week. What is the difference between the future value of Mary's investment extra \$50000 she needs for her dream home?

you are so great, super.

### 2 個解答

• 5 年前
最愛解答

先澄清兩點：

(1) 是否 10.5% p.a.

(2) 你是否假設一年有 52 個星期？

〔這個不同的假設會影響計算，因為若是的話，那 two-month compounded rate is 10.5%/26〕

2015-06-18 11:27:38 補充：

For each year, assume that there are 52 weeks.

Then for two years, there are 104 weeks, that is, 52 two-weeks period.

Consider a time line (vertical illustrated below) with each time unit being 2 weeks.

０＋

｜

１＋　＜－－　＄９００

｜

２＋　＜－－　＄９００

｜

３＋　＜－－　＄９００

｜

．．．

｜

５１＋　＜－－　＄９００

｜

５２＋　＜－－　＄９００

｜

ｖ

For every two weeks, the interest rate is i = 10.5%/26.

The amount of money Mary can accumulated is

\$900(1 + i)⁵¹ + \$900(1 + i)⁵⁰ + ... + \$900(1 + i)² + \$900(1 + i) + \$900

= \$900 + \$900(1 + i) + \$900(1 + i)² + ... + \$900(1 + i)⁵⁰ + \$900(1 + i)⁵¹

= \$900[(1 + i)⁵² - 1] / [(1 + i) - 1]

= \$900[(1 + i)⁵² - 1] / i

= \$51960.57972

The difference is

\$51960.57972 - (\$500000 - \$450000)

= \$51960.57972 - \$50000

= \$1960.57972

• 匿名
5 年前

我也是這樣想,假設一年有 52 個星期..

The answer is \$51960.58 and \$1960.58