A wishes to accumulate exactly $15,000 in a fund that credits interest at a nominal annual...

A wishes to accumulate exactly $15,000 in a fund that credits interest at a nominal annual rate of 6% compounded semiannually. A makes annual deposits of $1,000 at the beginning of each year into the fund, plus a final smaller deposit one year after the last $1,000 deposit. In which of the following ranges is the amount of the final deposit?

Expert Solution

Effective Interest Rate or EAR = [{1+(APR/n)}^n]-1

Where, APR = Annual Interest Rate or Nominal Rate, n = Number of times compounded in a year

Therefore,

For Semi Annual,

EAR = [{1+(0.06/2)}^2]-1 = 0.0609 = 6.09%

Period	Deposit/(Withdrawal) [beginning of period]	Opening Balance [Previous Closing+/-Deposit/Withdrawal]	Interest [Opening Balance*(0.0609)]	Closing Balance [Opening Balance+Interest]
1	1000	1000	60.9	1060.9
2	1000	2060.9	125.50881	2186.40881
3	1000	3186.40881	194.0522965	3380.461107
4	1000	4380.461107	266.7700814	4647.231188
5	1000	5647.231188	343.9163793	5991.147567
6	1000	6991.147567	425.7608868	7416.908454
7	1000	8416.908454	512.5897249	8929.498179
8	1000	9929.498179	604.7064391	10534.20462
9	1000	11534.20462	702.4330612	12236.63768
10	1000	13236.63768	806.1112347	14042.74891
11	=15000-14042.75 = $957.25	15000

Therefore, Last Small Deposit = $957.25

jeff jeffy answered 2 years ago

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