Unknown Investment Periods-Annuities Determine the number of periods for which t
ID: 2480950 • Letter: U
Question
Unknown Investment Periods-Annuities Determine the number of periods for which the following annuity payments would have to be invested to accumulate to $20,000. Assume payments are made at the end of each period. Convert the number of periods to years. (Click here to access the FV table to use with this problem.) Round the number of periods to the nearest whole number, and round the number of years to one decimal place.
1.Annual payments of $5,927 at 12% per annum, compounded annually.
______periods
_______year(s)
2.Semiannual payments of $3,409 at 16% per annum, compounded semiannually.
_______periods
________year(s)
3.Quarterly payments of $4,640 at 20% per annum, compounded quarterly.
_______periods
________year(s)
Explanation / Answer
Answer for question no:1.
Amount at the time of maturity =$20,000.
Annual payments =$5,927.
Interest per annum=12%.
Compounding annually.
Future value of an annuity = $20,000
Annual payment * Future value of $1 @12% for n periods =$20,000
Future value of $1 @12% for n periods =$20,000/Annual payment
=$20,000/$5,927
=3.374.
Referring to the annuity table the value appears at the intersection of 12% and 3 years. Number of periods=3.
Number of years = 3.
Answer for question no.2:
Semi annual payments of $3409.
Annual interest rate=16%.
Semi annual interest rate=16%/2 =8%.
Future value of the annuity =$20,000.
Semi annual payment * Future value of $1 @8% for n periods =$20,000
Future value of $1 @8% for n periods =$20,000/Semi annual payment
=$20,000/$3,409.
=5.8668.
Referring to the annuity table, in the column of 8%, 5.8668 is found where n=5. There fore number of periods =5 and number of years =5/2 =2.5 years
Answer for question no.3:
Quarterly payments =$4640.
Interest per annum=20%.
Interest per quarter =20%/4 =5%.
Future value of the annuity =$20,000.
Quarterly payment * Future value of $1 @5% for n periods =$20,000
Future value of $1 @5% for n periods =$20,000/Quarterly payment.
=$20,000/$4,640
=4.3103
referring to the FV table in the column where the interest is 5%, the value of 4.310 appears where n=4, therefore number of periods =4 and the number of years =4/4 =1 year.
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