Question

Two years ago, on July 2nd, 2018 you started saving for a bike. At that time, you made your first of a sequence of 5 consecutive equal deposits to pay for the bike. Today, on July 2nd 2020, your dad is chipping in $500 to help you along your way to your goal of having $10,000 in four years time (which will be July 2nd, 2024). Today, you made your third, out of the five deposits. Figure out what the deposits are such that you reach your goal. The interest rate over the entire period is 9%.

Answer 1

Let the annual deposit be A.

Computation of future value of deposits:

Date	Cash Deposit (C)	Computation of FV Factor	FV Factor @ 9 % (F)	FV (C x F)
July 2nd, 2018	A	(1+0.09)6	1.677100110841	A x 1.677100110841
July 2nd, 2019	A	(1+0.09)5	1.5386239549	A x 1.5386239549
July 2nd, 2020	A+500	(1+0.09)4	1.41158161	(A+ 500) x 1.41158161
July 2nd, 2021	A	(1+0.09)3	1.295029	A x 1.295029
July 2nd, 2022	A	(1+0.09)2	1.1881	A x 1.1881
July 2nd, 2023	0	(1+0.09)1	1.09	0
July 2nd, 2024	0	(1+0.09)0	1	0
			Total FV	A x 7.110434676 + $ 705.790805

Total future value of savings = A x (1.677100110841 + 1.677100110841 + 1.41158161 + 1.295029 + 1.1881) + $ 500 x 1.41158161

= A x 7.110434676 + $ 705.790805

A x 7.110434676 + $ 705.790805 = $ 10,000

A x 7.110434676 = $ 10,000 - $ 705.790805

                            = $ 9294.209195

A = $ 9,294.209195/7.110434676

   = $ 1,307.122506 or $ 1,307.12

Each 5 consecutive deposits should be of $ 1,307.12