Question

Compute the Future Values of the following. first assuming that payments are made on the last day of the period, and then assuming payments are made on the first day of the period:

payment	years	interest rate	Future Value (payment on last day )	Future Value (payment on first day )
$123	13	13%
$4,555	8	8%
$74,484	5	10%
$189,262	9	1%

What is the future value of payments of $189,262 for 9 years with an interest rate of 1% if the payments occur on the first day of the period?

Answer 1

If payments are made at the end of the period:

a. Future value is computed as follows:

Future value = Annual payment x [ [ (1 + r)ⁿ – 1 ] / r ]

= $ 123 x [ [ (1 + 0.13)¹³ - 1 ] / 0.13 ]

= $ 123 x 29.98470079

= $ 3,688.12 Approximately

b. Future value is computed as follows:

Future value = Annual payment x [ [ (1 + r)ⁿ – 1 ] / r ]

= $ 4,555 x [ [ (1 + 0.08)⁸ - 1 ] / 0.08 ]

= $ 4,555 x 10.63662763

= $ 48,449.84 Approximately

c. Future value is computed as follows:

Future value = Annual payment x [ [ (1 + r)ⁿ – 1 ] / r ]

= $ 74,484 x [ [ (1 + 0.10)⁵ - 1 ] / 0.10 ]

= $ 74,484 x 6.1051

= $ 454,732.27 Approximately

d. Future value is computed as follows:

Future value = Annual payment x [ [ (1 + r)ⁿ – 1 ] / r ]

= $ 189,262 x [ [ (1 + 0.01)⁹ - 1 ] / 0.01 ]

= $ 189,262 x 9.368527268

= $ 1,773,106.21 Approximately

If payments are made at the beginning of the period:

a. Future value is computed as follows:

Future value = Annual payment x [ [ (1 + r)ⁿ – 1 ] / r ] x (1 + r)

= $ 123 x [ [ (1 + 0.13)¹³ - 1 ] / 0.13 ] x 1.13

= $ 123 x 29.98470079 x 1.13

= $ 4,167.57 Approximately

b. Future value is computed as follows:

Future value = Annual payment x [ [ (1 + r)ⁿ – 1 ] / r ] x (1 + r)

= $ 4,555 x [ [ (1 + 0.08)⁸ - 1 ] / 0.08 ] x 1.08

= $ 4,555 x 10.63662763 x 1.08

= $ 52,325.83 Approximately

c. Future value is computed as follows:

Future value = Annual payment x [ [ (1 + r)ⁿ – 1 ] / r ] x (1 + r)

= $ 74,484 x [ [ (1 + 0.10)⁵ - 1 ] / 0.10 ] x 1.10

= $ 74,484 x 6.1051 x 1.10

= $ 500,205.50 Approximately

d. Future value is computed as follows:

Future value = Annual payment x [ [ (1 + r)ⁿ – 1 ] / r ] x (1 + r)

= $ 189,262 x [ [ (1 + 0.01)⁹ - 1 ] / 0.01 ] x 1.01

= $ 189,262 x 9.368527268 x 1.01

= $ 1,790,837.27

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