Question

Emily Dorsey's current salary is $84000 per year, and she is planning to retire 20 years from now. She anticipates that her annual salary will increase by 2000 each year ($84000 the first year, to $86000 the second year, $88000 the third year, and so forth), and she plans to deposit 5 % of her yearly salary into a retirement fund that earns 4 % interest compounded daily. What will be the amount of interest accumulated at the time of Emily's retirement? Assume 365 days per year.

The amount of interest accumulated at the time of Emily's retirement will be $ 48 Thousand. (Round to the nearest whole number.)

Please explain thoroughly. Preferably using the formulas not excel.

Answer 1

The first payment = 5% of $ 84,000

First payment = 0.05 x $ 84,000

First payment = $ 4200

The growth rate in the deposit = ( 100 x 100 ) 4200

The growth rate in the deposit = 2.38%

Futue value of growing annuity = A [ (1+r)ⁿ -(1+g)ⁿ ] r - g

FVA = $ 4200 [ (1+(0.04/365))^365x20 - (1+0.0238)²⁰ ] 0.04 - 0.0238

FVA = $ 161,959.26

The amount of interest accumulated at the time of Emily's retirement will be $ = $ 161,959.26 - $ 103,000

The amount of interest accumulated at the time of Emily's retirement will be $ = $ 58,959

Year	Deposit
1	4200
2	4300
3	4400
4	4500
5	4600
6	4700
7	4800
8	4900
9	5000
10	5100
11	5200
12	5300
13	5400
14	5500
15	5600
16	5700
17	5800
18	5900
19	6000
20	6100
	Total = 103,000