New home buyer planning for repairs problem

[Everydaylearner]

Hey guys so the correct answer is 22846.23 (which I did not get and guessed out of frustration). What I did was use the fv formula on the $1800 with the compounded 9% each year for 10 years. I got a total of $27347.27. Then with this amount I used the PV formula going back 10 years with the 3% interest rate and I got a total of 20,348.94. Any clarification on where I went wrong would be great! Thank you.

 

[BigBeachBanana]

It's a geometric increasing annuity, you can't simply FV 9%. It's helpful to write out the payments.
[math]PV=\frac{1800}{1.03}+\frac{1800\cdot1.09}{1.03^2}+...+\frac{1800\cdot1.09^9}{1.03^{10}}\\ PV=\frac{1800}{1.03}\cdot\left( 1+ \frac{1.09}{1.03}+...+ \left(\frac{1.09}{1.03}\right)^{9}\right)\\ \text{Let}\medspace v= \frac{1.09}{1.03}\\ PV=\frac{1800}{1.03}(1+v+...+v^{9})=\frac{1800}{1.03}\cdot\frac{1-v^{10}}{1-v}=22,846.2271[/math]PS: For annuity questions, you'll only need to write out your PV/FV cash flows and use the sum of geometric series. It'll solve 99% of your annuity questions.

 

[Everydaylearner]

It's a geometric increasing annuity, you can't simply FV 9%. It's helpful to write out the payments.
[math]PV=\frac{1800}{1.03}+\frac{1800\cdot1.09}{1.03^2}+...+\frac{1800\cdot1.09^9}{1.03^{10}}\\ PV=\frac{1800}{1.03}\cdot\left( 1+ \frac{1.09}{1.03}+...+ \left(\frac{1.09}{1.03}\right)^{9}\right)\\ \text{Let}\medspace v= \frac{1.09}{1.03}\\ PV=\frac{1800}{1.03}(1+v+...+v^{9})=\frac{1800}{1.03}\cdot\frac{1-v^{10}}{1-v}=22,846.2271[/math]PS: For annuity questions, you'll only need to write out your PV/FV cash flows and use the sum of geometric series. It'll solve 99% of your annuity questions.

Thanks for the equations Banana! Your explanation helped out alot!

 

[BigBeachBanana]

Thanks for the equations Banana! Your explanation helped out alot!

No problem. That's how annuity questions should be solved.