Question

How much would you have to invest today to receive the following? Use Appendix B or Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods.

  
a. $15,500 in 12 years at 11 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

b. $20,000 in 19 years at 7 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

c. $8,100 each year for 18 years at 15 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

d. $56,000 each year for 25 years at 8 percent. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
  

Answer 1

a

Future value = present value*(1+ rate)^time

15500 = Present value*(1+0.11)^12

Present value = 4430.533

b

Future value = present value*(1+ rate)^time

20000 = Present value*(1+0.07)^19

Present value = 5530.167

c

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 8100*((1-(1+ 15/100)^-18)/(15/100))

PV = 49636.52

d

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 56000*((1-(1+ 8/100)^-25)/(8/100))

PV = 597787.47

Answer 2

SOLUTION :

a.

FV = 15500

n = 12 years

r = 11% = 0.11 in decimals

=> 1 + r = 1.11

So, 

PV 

= FV / (1 + r)^n

= 15500 / 1.11^12

= 4430.53 ($)

Amount to are invested today = $4,430.53 (ANSWER)

b.

FV = 20000

n = 19 years

r = 7% = 0.07 in decimals

=> 1 + r = 1.07

So, 

PV 

= FV / (1 + r)^n

= 20000 / 1.07^19

= 5530.17 ($)

Amount to are invested today = $5,530.17 (ANSWER).

c.

Annual investment, A = 8100 ($)

Period, n = 18 years

r = 15% = 0.15 in decimals

=> (1 +r) = 1.15

PV 

= A ((1+r)^n) - 1) / (r*(1+r)^n)

= 8100(1.15^18 - 1) / (0.15*1.15^18)

= 49636.52 ($) 

PV of annual investments of $8,100 for 18 years @ 15% would be = $49,636.52 (ANSWER)

d.

Annual investment, A = 56000 ($)

Period, n = 25 years

r = 8% = 0.08 in decimals

=> (1 +r) = 1.08

PV 

= A ((1+r)^n) - 1) / (r*(1+r)^n)

= 56000(1.08^25 - 1) / (0.08*1.08^25)

= 597787.47 ($) 

PV of annual investments of $56,000 for 25 years @ 8% would be = $597,787.47 (ANSWER)