Suppose we would like to establish an annual prize of $100 for the student who gives the
best answer to the financial maths component of their Mathematics 1MA exam. How
much money would be required to establish a fund to pay this amount annually, with
the first payment in one year’s time if the money is invested at 7% p.a. compounded
every six months.
These formulae may be useful in this question:
sn| i =((1 + i)^n − 1)/i
an| i =(1 − (1 + i)^−n)/i
maths problem (interest))
2008-06-16 10:13 pm
回答 (1)
2008-06-16 11:42 pm
✔ 最佳答案
Let the principal amount be P.one year later, the interest must be able to cover the prize of $100
Thus, 100 = P*(1+0.07/2)*(1+0.07/2)
for the interest rate is compounded half-yearly.
Use calculator for amount of P here.
After first payment, the saving drops back to P,
and after the second year, the interest is $100 again,
exactly enough to pay for second payment.
and so on...
2008-06-16 15:43:48 補充：
A typo, the key equation should be
100 = P*(1+0.07/2)*(1+0.07/2) -P
收錄日期: 2021-04-25 13:52:26
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