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Present Value
Present Value. Sarah Wiggum would like to make single investment and have $2.3 million at the time of her retirement in 32 years. She has found a mutual fund that will earn 5 percent annually. How much will Sarah have to invest today? If Sarah earned an annual return of 15 percent, how soon could she then retire?
A - If Sarah can earn 5 percent annually for the next 32 years, the amount of money she will have to invest today is $_________
Solving for N - How many years will it take for $510 to grow to $1044.13 if its invested at 9 percent compounded annually?
A- The number of years it will take for $510 to grow to $1044.13 at 9 percent compounded annually is ____ years.
Expert Solution
A. Computation of Present Value using PV Function in Excel:
=-pv(rate,nper,pmt,fv)
Here,
PV = Present Value = ?
Rate = 5%
Nper = 32 years
PMT = 0
FV = $2,300,000
Substituting the values in formula:
=-pv(5%,32,0,2300000)
PV or Present Value = $482,692.18
So, If Sarah can earn 5 percent annually for the next 32 years, the amount of money she will have to invest today is $482,692.18
Computation of Time she will take for her retirement using NPER Function in Excel:
=nper(rate,pmt,-pv,fv)
Here,
NPER = Number of Periods = ?
Rate = 15%
PMT = 0
PV = $482,692.18
FV = $2,300,000
Substituting the values in formula:
=nper(15%,0,-482692.18,2300000)
Nper or Number of Periods = 11.17 years or 11.2 years
So, she can retire in 11.2 years.
A. Computation of Number of Years using NPER Function in Excel:
=nper(rate,pmt,-pv,fv)
Here,
NPER = Number of Years = ?
Rate = 9%
PMT = 0
PV = $510
FV = $1,044.13
Substituting the values in formula:
=nper(9%,0,-510,1044.13)
Nper or Number of Years = 8.31 years
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