For this case we have an equation of the form:

Where,
A: initial amount
b: growth rate
x: number of years
Substituting values we have:

By the time the earnings increase to 75000 we have:

From here, we clear x:
Answer:
you will have to wait until 23.95 years your winnings are worth $ 75,000
Answer:
$ 226.04
Explanation:
Given:
Paying fund, FV = $ 30000
Interest rate, i = 2%
Time, t = 10 years
Now,
![\textup{PMT}=\textup{FV}[\frac{i}{(1+i)^n-1}]](https://tex.z-dn.net/?f=%5Ctextup%7BPMT%7D%3D%5Ctextup%7BFV%7D%5B%5Cfrac%7Bi%7D%7B%281%2Bi%29%5En-1%7D%5D)
since, the payment is made monthly
thus,
n = 10 × 12 = 120 months
i = 2% / 12 = 0.02 / 12
on substituting the values in the above equation, we get
![PMT={30000}[\frac{\frac{0.02}{12}}{(1+{\frac{0.02}{12}})^{120}-1}]](https://tex.z-dn.net/?f=PMT%3D%7B30000%7D%5B%5Cfrac%7B%5Cfrac%7B0.02%7D%7B12%7D%7D%7B%281%2B%7B%5Cfrac%7B0.02%7D%7B12%7D%7D%29%5E%7B120%7D-1%7D%5D)
or
PMT = $ 226.04
Answer:
c. $980,200
Explanation:
The computation of the cash collections is shown below:
As January sales is $839,000
So, Cash sales
= $839,000 × 20%
= $167,800
So Credit sales
= $839,000 × 80% × 75%
= $503,400
And on January 1 , the account receivable is $309,000
So, the January cash collections from sales is
= $167,800 + $503,400 + $309,000
= $980,200
Answer:
Explanation:
Duration is used to determine a bond's price sensitivity to interest rate changes. For fixed rate bonds, an increase in market interest rates leads to a decrease in the price of a bond. On the other hand, a decrease in market interest rates leads to an increase in the price of a bond. The longer the duration, the greater the swings in a bond price for a given change in interest rates. There are various types of duration. Two well-known types used for straight bonds (i.e., bonds without embedded options) are Macauley Duration and Modified Duration. Macauley duration is the weighted average of the time until cash flow dates, where the weights are given by the fraction of the present value arising from that period's cash flow. Modified Duration is derived from Macauley Duration.
Answer and Explanation:
The formula used to calculate Macauley Duration is shown below:
{eq}Duration = t_1 * \frac{c * d(t_1)}{PV} + t_2 * \frac{c * d(t_2)}{PV} + ...