What is the present value of an ordinary annuity that pays 250 dollars per year
ID: 2775008 • Letter: W
Question
What is the present value of an ordinary annuity that pays 250 dollars per year for 4 years, if the appropriate discount rate is 5.0 percent per year, compounded annually?
What is the future value (at the end of 4 years) of an ordinary annuity that pays 250 dollars per year if the appropriate discount rate is 5.0 percent per year, compounded annually?
What is the present value of an ordinary annuity that pays $40 every 6 months, for 10 years, if the interest rate is 8.0 percent per year, compounded semi-annually?
What is the present value of an annuity due that pays 250 dollars per year for 4 years, if the appropriate discount rate is 5.0 percent per year, compounded annually?
If you receive $100,000 in a lump sum, how much could you withdraw each year, starting one year from today, if you wish to receive 10 payments? The interest rate is 5 1/8 percent per year, compounded annually.
Explanation / Answer
1)
Computing present value of ordinary annuity is as follows:
Year
Deposit
Interest
Cash flow
Annuity factor @5%
Discounted flows
1
250
12.5
262.5
1.8594
488
2
262.5
13.125
275.625
2.723
751
3
275.625
13.78125
289.4063
3.545
1,026
4
289.4063
14.47031
303.8766
4.329
1,315
3,580
Hence, it is $3,580.
2)
Computing future value of ordinary annuity is as follows:
Year
Deposit
Interest
Cash flow
Future Annuity factor @5%
Future cash flows
1
250
12.5
262.5
1.05
276
2
262.5
13.125
275.625
2.152
593
3
275.625
13.78125
289.4063
3.31
958
4
289.4063
14.47031
303.8766
4.525
1,375
3,202
Hence, it is $3,202.
Year
Deposit
Interest
Cash flow
Annuity factor @5%
Discounted flows
1
250
12.5
262.5
1.8594
488
2
262.5
13.125
275.625
2.723
751
3
275.625
13.78125
289.4063
3.545
1,026
4
289.4063
14.47031
303.8766
4.329
1,315
3,580
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