Question

derek will deposit $4,566 per year for 10 years into an account that earns 14 %. Assuming the first deposit is made 7 years from today how much will be in the account 37 years from today ?

Answer 1

Firstly, let's understand the timeline-

7 years from now he will start depositing $4566

17 years from now he will stop depositing the money

We need to find the Future value of these deposits 37 years from now.

Now, we will first calculate the Future value of the deposits 17 years from now-

Years from now	Years left to 17 years	Deposits	FV
7	10	4566	16,927.17
8	9	4566	14,848.40
9	8	4566	13,024.91
10	7	4566	11,425.36
11	6	4566	10,022.25
12	5	4566	8,791.44
13	4	4566	7,711.79
14	3	4566	6,764.73
15	2	4566	5,933.97
16	1	4566	5,205.24
Interest rate	14%
Amount that Derek will have 17 years from now	100,655.26

Now to find the value 37 years year from now we will use the Time value of money formula -

Future Value = Present value*((1+interest rate)^time)

Value 37 years from now = Value 17 years from now*((1+interest earned)^(37-17))

= $100,655.26*(1.14^20)

= $ 1,383,354.573