A couple thinking about retirement decide to put aside $2,100 each year in a savings plan that earns 7% interest. In 10 years th
1 answer:
Answer:
310,588.5
Explanation:
As is not said we can assume the 2,100 each year to be paid at the end of the year, and the 7% to be used as a compunded anually rate. So let´s first think just about the 2,100, as they are regulary payments, they can be seen as an anuity inmediate, the formula is as follows:
where sn is the future value of the regular payments, i is the interest rate and n is the number of payments and p is the amount of regular payment so in this particular case we have:
=198,367.65
So now let´s think on the gift of 29,000 as it is paid on 10 years, there will remain 20 years with an investment rate of 7% compounded anually. so there we have the classic formula of future value
where FV is the future value, PV is the present value, i is the interest rate per period, and n is the number of periods. Again in this particular case we have:
so the total amont will be:
total=198,367.65+112,220.85
total=310,588.5
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Answer:
The world's population would have been 7.1137 billion in 2012, and this is 0.0437 billion (i.e. 7.1137 - 7.07 = 0.0437) higher compared to the population reference bureau estimate of 7.07 billion in July 2012.
Explanation:
This can be computed using the following exponential formula:
P(t) = P(0)a^t ............................ (1)
Where;
P(t) = World population in year t.
P(0) = World population in year 0 which is 1998 = 5.937 billion
a = base = ?
t = number of years
Substituting the value into equation (1), we have:
P(t) = 5.937 * a^t .......................................... (2)
Since we have 10 years from 1998 to 2008 (i.e. 2008 - 1998 = 10), we have:
P(t) = P(10) = World population in 2008 = 6.771 billion
t = 10
Substituting the value into equation (2) and solve for a, we have:
6.771 = 5.937 * a^10
a^10 = 6.771 / 5.937
a^10 = 1.1405
a =
a = 1.013
Since we have 14 years from 1998 to 2012 (i.e. 2012 - 1998 = 14), we now have:
P(t) = P(14) = World population in 2012 = ?
P(0) = World population in year 0 which is 1998 = 5.937 billion
a = 1.013 as already calculated above
t = 14
Substituting the value into equation (1), we have:
P(14) = 5.937 * 1.013^14
P(14) = 5.937 * 1.192
P(14) = 7.1137 billion
Therefore, the world's population would have been 7.1137 billion in 2012, and this is 0.0437 billion (i.e. 7.1137 - 7.07 = 0.0437) higher compared to the population reference bureau estimate of 7.07 billion in july 2012.