You need $24,656 at the end of 7 years, and your only investment outlet is an 8
ID: 2784689 • Letter: Y
Question
You need $24,656 at the end of 7 years, and your only investment outlet is an 8 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.)
Single Payment Made _____
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.)
Amount to be Paid______
Appendix B Present value of $1,PVF PV=FV Percent Period 4 Appendlx B (concluded) Percent Period 50% 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 0.640 0.592 0.549 0.510 0.444 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 0512 0.455 0.406 0.364 0.296 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335 0.262 0.207 0.165 0.133 0.088 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 0.210 0.159 0.122 0.095 0.059 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135 0.086 0.056 0.037 0.025 0.012 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065 0.035 0.020 0.011 0.006 0.002 0.125 0.108 0.093 0.080 0.069 0.060 0.052 0.045 0.023 0.012 0.006 0.003 0.001 0.098 0.083 0.070 0.060 0.051 0.043 0.037 0.031 0.014 0.007 0.003 0.002 0 0.087 0.073 0.061 0.051 0.043 0.037 0.031 0.026 0.012 0.005 0.002 0.001 0 0.047 0.038 0.030 0.024 0.020 0.016 0.013 0.010 0.004 0.001 0.001 0 0.026 0.020 0.015 0.012 0.009 0.007 0.005 0.004 0.001 0Explanation / Answer
We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
1.
24656=P(1.08)^7
Hence
P=$24656/1.08^7
=$14386.54(Approx).
2.
We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
Hence
24656=P(1.08)^6+P(1.08)^5+P(1.08)^4+.........+P(1.08)^1+P
24656=P[1.08^6+1.08^5+..........+1.08^1+]1
24656=P*8.92280336
P=24656/8.92280336
=$2763.26(Approx)
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