Question

4. Suppose you are hired on January 1, 2020 and start depositing $400 at the end of each month, with the first deposit on February 1, 2020, in a pension fund that pays interest of 9% per year compounded monthly on the minimum monthly balance and credited at the end of each month.  

(a) How much money is in the pension fund on March 1, 2020?

(b) How much money is in the pension fund on April 1, 2020?

(c) How much money will be in the pension fund on January 1, 2040?

(d) What is the total amount of interest earned in this pension fund during these 20 years?

Answer 1

FV of Annuity :
Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

a

Particulars	Amount
Cash Flow	400
Int Rate	0.750%
Periods	2

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
=400 * [ [(1+0.0075)^2] - 1 ] / 0.0075
=400 * [ [(1.0075)^2] - 1 ] /0.0075
=400 * [ [1.0151] - 1 ] / 0.0075
=400 * [0.0151] /0.0075
803.00

b

Particulars	Amount
Cash Flow	400
Int Rate	0.750%
Periods	3

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
=400 * [ [(1+0.0075)^3] - 1 ] / 0.0075
=400 * [ [(1.0075)^3] - 1 ] /0.0075
=400 * [ [1.0227] - 1 ] / 0.0075
=400 * [0.0227] /0.0075
1209.02

c

Particulars	Amount
Cash Flow	400
Int Rate	0.750%
Periods	240

FV of Annuity = Cash Flow * [ [(1+r)^n ] - 1 ] /r
=400 * [ [(1+0.0075)^240] - 1 ] / 0.0075
=400 * [ [(1.0075)^240] - 1 ] /0.0075
=400 * [ [6.0092] - 1 ] / 0.0075
=400 * [5.0092] /0.0075
267154.75

d

Total Interest received = FV of annuity - monthly payments

= 267154.75 - (400*12*20)

= 267154.75 - 96000

= $ 171154.75

Pls do rate, if the answer is correct and comment, if any further assistance is required.