Question

You deposit today $3100 dollars in an account that pays 4.8 percent per year. For the next few years you will keep making deposits 7.1 percent larger than the previous one. What will be the balance on the account after 15 deposits. I feel like I am missing the annuity to solve this problem, but I could be wrong.

Answer 1

Today I deposit $3,100. Which earns return annually at 4.8%. Thus in the first year the return is $149. 3100*4.8% 3100+149 = 3249.

Every year I go on depositing and I increase the deposit by 7.1%. Thus 3100*(1.071) = 3320. After the 2nd deposit the balance will be 3249 which is the amount deposited plus the interest, and in that year I deposit 3320. Thus the balance will be previous years interest earned income plus this years deposit. Which is $6569 (3320+3249). The interest on that will 6569(1.048) = $6,884

	Deposit	Total balance (Deposit plus previous years return)	Return
Initial deposit	3100		3249
	3320	6569	6884
	3556	10440	10941
	3808	14749	15457
	4079	19536	20474
	4368	24842	26035
	4678	30713	32187
	5011	37198	38983
	5366	44350	46478
	5747	52226	54733
	6155	60888	63811
	6592	70403	73782
	7060	80843	84723
	7562	92285	96715
	8099	104813	109844

Thus the balance would be $109844 including return.

Not including return it would be $104813