Question

You would like to open a business in 3 years. This business will require $500,000 to startup. How much should you deposit at the end of each month for the next three years into an account so that you will have the required $500,000 at the end of three years. This account already has $100,000 in it. The interest rate is 6% compounded monthly.

Answer 1

Given present account balance= 100000

Future value of current account balance = 100000*(1+ interest rate/n)*time*n

Given time = 3 years

n= number of compunding = 12

Interest rate =6%

hence future value= 100000*(1+6%/12)^(3*12)

=100000*(1.005)^36

=100000*1.19668

=119668

Hence Balance amount which is required to be funded through monthly deposit = 500000-119668= 380332

Hence let the amount to be deposited every month be x in order to achive a future value of the remaining amount .

Hence future value of amount deposited monthly is given as = X * Future value of annuity factor for 36 months at 0.5% interest per month

the future value of annuity factor due at the end of the month is determined as =

Months	Future value at 0.5%
N	(1+ 0.005)^(N-1)
1	1
2	1.005
3	1.010025
4	1.015075125
5	1.020150501
6	1.025251253
7	1.030377509
8	1.035529397
9	1.040707044
10	1.045910579
11	1.051140132
12	1.056395833
13	1.061677812
14	1.066986201
15	1.072321132
16	1.077682738
17	1.083071151
18	1.088486507
19	1.09392894
20	1.099398584
21	1.104895577
22	1.110420055
23	1.115972155
24	1.121552016
25	1.127159776
26	1.132795575
27	1.138459553
28	1.144151851
29	1.14987261
30	1.155621973
31	1.161400083
32	1.167207083
33	1.173043119
34	1.178908334
35	1.184802876
36	1.19072689
Total	39.33610496

Hence Future Value = x* 39.33610496

380332= x* 39.33610496

x=380332/39.33610496

=9668.77

Hence the required amount to be deposited at the end of each mont for 3 years = 9668.77

(Note it is assumed that the first payment will be made at the end of each month and the last monthly payment will be made at the end of 36th month)