Question

Derek currently has $11,132.00 in an account that pays 4.00%. He will withdraw $5,347.00 every other year beginning next year until he has taken 4.00 withdrawals. He will deposit $11132.0 every other year beginning two years from today until he has made 4.0 deposits. How much will be in the account 23.00 years from today?

Answer 1

Assumptions made:

It is assumed that:

i) The deposits and withdrawals are made at the beginning of the year.

ii) The interest is paid at the end of the year.

Derek's Bank Account ( Roughly for calculations)
Dr					Cr
Date	Particulars	$	Date	Particulars	$
1st April, 2019	Balance b/d	11132
31st Mar, 2020	Interest Received a/c	445.28	31st Mar, 2020	Balance c/d	11577.28
		11577.28			11577.28
1st April, 2020	Balance b/d	11577.28	1st April, 2020	Cash (withdrawal made)	5347
31st Mar, 2021	Interest Received a/c	249.22	31st Mar, 2021	Balance c/d	6479.5
		11826.5			11825.5
1st April 2021	Balance b/d	6479.5	1st April, 2021	Cash (withdrawal made)	5347
1st April 2021	Cash (Deposit)	11132	31st Mar 2022	Balance c/d	12755.08
31st Mar 2022	Interest Received a/c	490.58
		18102.08			18102.08
1st April 2022	Balance b/d	12755.08	1st April 2022	Cash (withdrawal made)	5347
1st April 2022	Cash (Deposit)	11132	31st Mar 2023	Balance c/d	19281.69
31st Mar 2023	Interest Received a/c	741.61
		24628.69			24628.69
1st April 2023	Balance b/d	19281.69	1st April 2023	Cash (withdrawal made)	5347
1st April 2023	Cash (Deposit)	11132	31st Mar 2024	Balance c/d	26069.36
31st Mar 2024	Interest Received a/c	1002.67
		31416.36			31416.36
1st April 2024	Balance b/d	26069.36	31st Mar 2025	Balance c/d	38689.42
1st April 2024	Cash (Deposit)	11132
31st Mar 2025	Interest Received a/c	1488.06
		38689.42			38689.42
1st April 2025	Balance b/d	38689.42

Future value = Present Value (1 + r) n

                =38689.42 (1 + 4%) 17

                =38689.42 x 1.95

                =75444.37

Working Notes:

1. Calculation of interest for the 1st year

Given that the interest is received at 4%. Therefore, the amount of interest received will be:

Interest received

= Principal amount x Rate of interest

= 11132 x 4%

=445.28

2. Calculation of interest for 2nd year

Interest received

                = Principal amount x Rate of interest

                = 6230.28 x 4%

                = 249.22

3. Calculation of interest for 3rd year

Interest received

                = Principal amount x Rate of interest

                =12264.5 x 4%

                =490.58

4. Calculation of interest for 4th year

Interest received

                = Principal amount x Rate of interest

                = 18540.08 x 4%

                =741.61

5. Calculation of interest for 5th year

Interest received

                = Principal amount x Rate of interest

                =25066.69 x 4%

                =1002.67

6. Calculation of interest for 6th year

Interest received

                = Principal amount x Rate of interest

                =37201.36 x 4%

                =1488.06

7. Calculation of future value of the amount after 23 years compounded annually at 4%

Future value = Present Value (1 + r) n

                =38689.42 (1 + 4%) 17

                =38689.42 x 1.95

                =75444.37

The n denotes the number of years. It is calculated as:

The current year is 2019. We have to find 23 years from this year. That is:

2019 + 23 = 2042

The account prepared shows the value upto 2025

So, n will be 2042 - 2025 = 17

This is how n = 17