Question

You inherit $30,000. For 12 years, the money is invested in a mutual fund earning an annual rate of return of 6.4%. For the next 16 years, you make monthly contributions of $400 at the end of each month. If the account yields a 5.7% APR compounded monthly during that time, what is the account balance immediately following the final deposit?

Answer 1

The amount of $30000 will be mature as follows:
Year	Amount Invest	Annual return	Balance
0	30,000	-	30,000
1	30,000	1,920	31,920
2	31,920	2,043	33,963
3	33,963	2,174	36,137
4	36,137	2,313	38,449
5	38,449	2,461	40,910
6	40,910	2,618	43,528
7	43,528	2,786	46,314
8	46,314	2,964	49,278
9	49,278	3,154	52,432
10	52,432	3,356	55,788
11	55,788	3,570	59,358
12	59,358	3,799	63,157
Now it is assumed that the above return of $ 63,157 will be re invest at the APR rate and will be mature as follows with monthly investment of $400
Now for next 16 years month wise table is as follows:

Month	Amount Invest	Monthly Amount	Rate of return	Return amount	Balance
0	63,157	-	0.0046	-	63,157
1	63,157	400	0.0046	294	63,851
2	63,851	400	0.0046	297	64,549
3	64,549	400	0.0046	301	65,249
4	65,249	400	0.0046	304	65,953
188	268,925	400	0.0046	1,247	270,573
189	270,573	400	0.0046	1,255	272,227
190	272,227	400	0.0046	1,262	273,890
191	273,890	400	0.0046	1,270	275,560
192	275,560	400	0.0046	1,278	277,237
At the end the investor will get the amount of $ 2,77,237

due to character constraint i have not pasted the entire table, but have pasted few initial years and few end years to justify my answer