Question

Suppose you were hired on January 1, 2017 and started depositing $300 at the end of
each month, with the first deposit on January 31, 2017, 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 was in the pension fund on March 1, 2017?

(b) How much money was in the pension fund on April 1, 2017?

(c) How much money will be in the pension fund on January 1, 2037?
(d) What is the total amount of interest earned in this pension fund during these 20 years?

Answer 1

(a) On March 1, 2017 2 months have passed so there have been two deposits and one at the end of January and one at the end of february so these and the interest on these will be there in the account:

As the payments are made at the end of the month, the february payment in not compounded.

(b)On April 1, 2017 3 months have passed so there have been three deposits and one at the end of January, one at the end of february, one at the end of march so these and the interest on these will be there in the account:

As the payments are made at the end of the month, the march payment in not compounded.

(c) On January 1, 2037, 20 years have passed, FV is calculated as follows:

We are given the following information:

Payment	PMT	$                  300.00
Rate of interest	r	9.00%
Number of years	n	20
Monthly Frequency	T	12
Fund value	FV	To be calculated

We need to solve the following equation to arrive at the required FV:

So the FV is $200366.06

(d) There were 12 x 20 = 240 payments of 300 each so total payments were 300 x 240 = 72000 so rest of the future value of the fund is the amount of interest which is 200366.06 -7200 =  $128,366.06