Question

Document1 - Word Acrobat Tell me what you want to do Аавьссо Normal лавьсах АавьсАавьссс Аав Аавьссс Аавьссо Аавьссо Аавьсери No Spac. Heading 1 Heading 2 T itle Subtitle Subtle Em... Emphasis Intense Styles Suppose you make monthly mortgage payments of $1,345 and have 11 years left on the mortgage (next payment due next month). Assuming a 4.5% stated annual interest rate for the mortgage, how much would you need today to pay off the mortgage? If you make an initial contribution of $8,000 to a retirement account 5 years from now and make annual contributions of $8,000 thereafter, after how many contributions will your balance have reached at least $1,000,000 if your account earns 6% annual interest?

Answer 1

For the mortgage payment part, we need to pay $139,831 today in order to clear the entire payment. The same is computed by taking out the Present Value of all the series of payment for next 132 months, i.e 11 years. I have presented working for first 1 year as word limits are exceeding for all the 11 years.

Formula used is 1345*(1+(0.045/12))^No of month

Month	Monthly Payment	PV @ 4.5%
1	1,345	1,340
2	1,345	1,335
3	1,345	1,330
4	1,345	1,325
5	1,345	1,320
6	1,345	1,315
7	1,345	1,310
8	1,345	1,305
9	1,345	1,300
10	1,345	1,296
11	1,345	1,291
12	1,345	1,286

Contribution to retirement account

The total contributions shall reach at least $1,000,000 after a total of 10 contributions as per the below table

Year	Contribution	Principal	Total	Interest	Total Balance at year end
5	8,000	-	8,000	480	8,480
6	8,000	8,480	16,480	989	17,469
7	8,000	17,469	25,469	1,528	26,997
8	8,000	26,997	34,997	2,100	37,097
9	8,000	37,097	45,097	2,706	47,803
10	8,000	47,803	55,803	3,348	59,151
11	8,000	59,151	67,151	4,029	71,180
12	8,000	71,180	79,180	4,751	83,931
13	8,000	83,931	91,931	5,516	97,446
14	8,000	97,446	105,446	6,327	111,773