Question

A company needs $48,000 in 4 years to replace two trucks. Find the amount it must deposit at the end of each quarter in a fund earning 6% compounded quarterly.

Answer 1

We are given the following information:

r	6.00%
n	4
T	4
FV	$48,000.00

We need to solve the following equation to arrive at the required FV
Here T is the frequency of interest in a year

So at the end of each quarter we need to deposit $2676.72 to have $48000 at the end of 4 years. We can even create a schedule to verify the same.

Quarter	Opening Balance	PMT	Interest	Closing Balance
1	$                           -	$ 2,676.72	$                     -	$           2,676.72
2	$              2,676.72	$ 2,676.72	$              40.15	$           5,393.60
3	$              5,393.60	$ 2,676.72	$              80.90	$           8,151.23
4	$              8,151.23	$ 2,676.72	$           122.27	$         10,950.22
5	$            10,950.22	$ 2,676.72	$           164.25	$         13,791.20
6	$            13,791.20	$ 2,676.72	$           206.87	$         16,674.79
7	$            16,674.79	$ 2,676.72	$           250.12	$         19,601.63
8	$            19,601.63	$ 2,676.72	$           294.02	$         22,572.38
9	$            22,572.38	$ 2,676.72	$           338.59	$         25,587.69
10	$            25,587.69	$ 2,676.72	$           383.82	$         28,648.23
11	$            28,648.23	$ 2,676.72	$           429.72	$         31,754.68
12	$            31,754.68	$ 2,676.72	$           476.32	$         34,907.72
13	$            34,907.72	$ 2,676.72	$           523.62	$         38,108.06
14	$            38,108.06	$ 2,676.72	$           571.62	$         41,356.40
15	$            41,356.40	$ 2,676.72	$           620.35	$         44,653.47
16	$            44,653.47	$ 2,676.72	$           669.80	$         48,000.00

• Opening balance = previous year's closing balance
• Closing balance = Opening balance+PMT+Interest
• PMT is calculated as per the above formula
• Interest = 0.06/4 x opening balance
• At the end of 16th quarter we will have $48000 in the fund as required