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Consider the following future value
Consider the following future value. (Round your answers to the nearest cent.) $3,725 st 11 % compounded monthly for 17 years and 7 months (a) Find the present value that will generate the given future value. $ (b) Interpret the present value. One would have to invest $ now to have the future value in the given time. Need Help? Watch It Submit Answer View Previous Question Question 8 of 9 View Next Question Home My Assignments + Request Extension
Consider the following future value. (Round your answers to the nearest cent.) $4,413 at 10% compounded quarterly for 4 years (a) Find the present value that will generate the given future value. $ 8615 x (b) Interpret the present value One would have to invest 1961.5 X now to have the future value in the given time. Need Help? with Submit Answer View Previous Question Question 9 of 9
Expert Solution
Future value = $3725
Rate = 11 7/8% = 11 + 7/8
Rate = 11 + 0.875 = 11.875%
Time = 17 years 7 months
Future value = Present value * ( 1 + r%)^t
Compounded monthly
Future value = Present value * ( 1 + r%/12)^t*12
3725 = Present value * ( 1 + 11.875%/12)^(17*12 +7)
3725 = Present value * ( 1 + 11.875%/12)^(211)
Present value = 3725 / ( 1 + 11.875%/12)^(211)
Present value = 3725 / ( 1 + 0.989583%)^(211)
Present value = 3725 / ( 1 + 0.00989583)^(211)
Present value = 3725 / ( 1.00989583)^(211)
Present value = 3725 / 7.986536
Present value = $466.41
One would have to invest $466.41 now to have the future value in the given time.
Future value = $4413
Rate = 10 3/4% = 10 + 3/4
Rate = 10 + 0.75 = 10.75%
Time = 4 years
Future value = Present value * ( 1 + r%)^t
Compounded quaterly
Future value = Present value * ( 1 + r%/4)^t*4
4413 = Present value * ( 1 + 10.75%/4)^(4*4)
4413 = Present value * ( 1 + 10.75%/4)^(16)
Present value = 4413 / ( 1 + 0.026875)^(16)
Present value = 4413 / ( 1.026875)^(16)
Present value = 4413 / 1.528555783
Present value = $2887.04
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