You need $25,156 at the end of 7 years, and your only investment outlet is an 7
ID: 2657286 • Letter: Y
Question
You need $25,156 at the end of 7 years, and your only investment outlet is an 7 percent long-term certificate of deposit (compounded annually). With the certificate of deposit, you make an initial investment at the beginning of the first year. Use Appendix B and Appendix C for an approximate answer, but calculate your final answer using the formula and financial calculator methods. a. What single payment could be made at the beginning of the first year to achieve this objective? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
b. What amount could you pay at the end of each year annually for 7 years to achieve this same objective? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
Explanation / Answer
a.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
25156=P(1.07)^7
P=25156/1.07^7
=$25156*0.622749741
=$15665.89(Approx).
2.
Future value of annuity=Annuity[(1+rate)^time period-1]/rate
25156=Annuity[(1.07)^7-1]/0.07
25156=Annuity*8.654021093
Annuity=25156/8.654021093
=$2906.86(Approx).
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