You will invest the following cash flows into an investment account on the following dates. TIME...

You will invest the following cash flows into an investment account on the following dates.

TIME CASH FLOWS --------------------------------------------------------------

1/1/23 +$6500

1/1/24 +$6500

1/1/25 +$6500

1/1/26 +$6500

1/1/27 +$6500

Assume an interest rate of 10%, compounded annually. (The stated rate is 10%, compounded annually.) How much will you have in your account on 1/1/27 the instant after you make that last investment of $6500 on 1/1/27?

Expert Solution

Interest rate = 10 %

Period	Cash Flows	Balance after Deposit	interest at 10 % On balance	Closing balance
01/01/2023	$ 6,500.00	$ 6,500.00	$ 650.00	$ 7,150.00
01/01/2024	$ 6,500.00	$ 13,650.00	$ 1,365.00	$ 15,015.00
01/01/2025	$ 6,500.00	$ 21,515.00	$ 2,151.50	$ 23,666.50
01/01/2026	$ 6,500.00	$ 30,166.50	$ 3,016.65	$ 33,183.15
01/01/2027	$ 6,500.00	$ 39,683.15

Balance after deposite on 01/01/27 = $ 39,683.15

or we can do in this way

Future value factor = (1 + interest rate) ^ n = 10 %

n - no. of the balance period of compounding years

Period	Bal Period of compounding years	CF	FVF @10%	FV of CFs
01/01/2023	4	$ 6,500.00	1.4641	$ 9,516.65
01/01/2024	3	$ 6,500.00	1.3310	$ 8,651.50
01/01/2025	2	$ 6,500.00	1.2100	$ 7,865.00
01/01/2026	1	$ 6,500.00	1.1000	$ 7,150.00
01/01/2027	0	$ 6,500.00	1.0000	$ 6,500.00
	Balance after deposit on 01/01/27			$ 39,683.15

Please comment if any further explanation required.

jeff jeffy answered 2 years ago

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