future value

[logistic_guy]

Don invested \(\displaystyle \$ 2000\) at \(\displaystyle 6\%\) compounded annually for \(\displaystyle 10\) years. Then, he found that he could earn a higher rate and for the next \(\displaystyle 30\) years his account earned \(\displaystyle 8\%\). Use a spreadsheet to find the future value of this investment at the end of \(\displaystyle 40\) years.

 

[jonah2.0]

Beer drenched reaction follows.

Don invested \(\displaystyle \$ 2000\) at \(\displaystyle 6\%\) compounded annually for \(\displaystyle 10\) years. Then, he found that he could earn a higher rate and for the next \(\displaystyle 30\) years his account earned \(\displaystyle 8\%\). Use a spreadsheet to find the future value of this investment at the end of \(\displaystyle 40\) years.

What have you done so far?

 

[logistic_guy]

Beer drenched reaction follows.

What have you done so far?

First time to use excel. I'm not sure if this is the correct way!

 

[khansaheb]

First time to use excel. I'm not sure if this is the correct way!

View attachment 39020

Your result of your calculations uptill this point is correct. You can check your output directly by using:

FV = PV * (1+i)^n ...→....... where the variables has their usual values.

Using the above and a calculator we get

FV₁₀
= 2000 *(1.06)¹⁰
= 3581.6953 = $ 3581.70

 

[logistic_guy]

Your result of your calculations uptill this point is correct. You can check your output directly by using:

FV = PV * (1+i)^n ...→....... where the variables has their usual values.

Using the above and a calculator we get

FV₁₀
= 2000 *(1.06)¹⁰
= 3581.6953 = $ 3581.70

Thanks for the share professor.

I continued the excel sheet and this is what I got:



The formula gives me:

\(\displaystyle F_V = 3581.695393(1 + 0.08)^{30} \approx 36041.37182\)

It fits perfectly with the excel sheet

 

[jonah2.0]

Beer drenched reaction follows.

Don invested \(\displaystyle \$ 2000\) at \(\displaystyle 6\%\) compounded annually for \(\displaystyle 10\) years. Then, he found that he could earn a higher rate and for the next \(\displaystyle 30\) years his account earned \(\displaystyle 8\%\). Use a spreadsheet to find the future value of this investment at the end of \(\displaystyle 40\) years.

First time to use excel. I'm not sure if this is the correct way!

View attachment 39020

As I was about to reply 6 minutes ago before you suddenly posted your new Excel stuff:

It's the correct way. You just needed to add two or more columns and some additional stuff for full automation of the rounding (to the nearest cent) using the odd-add rule of rounding to get 3581.70 instead of the theoretical 3581.69539309 ... Translation: That is the value at the end of 10 years using the rate of 6 percent compounded annually.

To arrive at the future value at the end of 40 years, you merely consider the value at the end of 10 years at the rate of 6 percent compounded annually as the beginning capital for the next 30 years at the rate of 8 percent compounded annually.

 

[jonah2.0]

Thanks for the share professor.

I continued the excel sheet and this is what I got:

View attachment 39021

The formula gives me:

\(\displaystyle F_V = 3581.695393(1 + 0.08)^{30} \approx 36041.37182\)

It fits perfectly with the excel sheet

\(\displaystyle 2000\bigg(1+\frac{0.06}{1}\bigg)^{10×1}\bigg(1+\frac{0.08}{1}\bigg)^{30×1}\)

 

[logistic_guy]

Beer drenched reaction follows.


As I was about to reply 6 minutes ago before you suddenly posted your new Excel stuff:

It's the correct way. You just needed to add two or more columns and some additional stuff for full automation of the rounding (to the nearest cent) using the odd-add rule of rounding to get 3581.70 instead of the theoretical 3581.69539309 ... Translation: That is the value at the end of 10 years using the rate of 6 percent compounded annually.

To arrive at the future value at the end of 40 years, you merely consider the value at the end of 10 years at the rate of 6 percent compounded annually as the beginning capital for the next 30 years at the rate of 8 percent compounded annually.

Thanks for the share professor jonah.

\(\displaystyle 2000\bigg(1+\frac{0.06}{1}\bigg)^{10×1}\bigg(1+\frac{0.08}{1}\bigg)^{30×1}\)

Beautiful shortcut