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Experts say that the baby boom generation (born 1946-1960) cannot count on a company pension or Social Security benefits to provide a comfortable retirement
Experts say that the baby boom generation (born 1946-1960) cannot count on a company pension or Social Security benefits to provide a comfortable retirement. It is recommended that they start to save regularly and early. Michael, a baby boomer, has decided to deposit $1000 every six months in an account that pays 12% compounded semiannually for 15 years.
a) How much money will be in the account at the end of the 15 years?
b) Suppose Michael has determined he needs to accumulate $120,000 from this annuity. What rate would achieve this goal?
c) If he cannot get the higher rate, what amount would his payments need to be in order to achieve the goal?
d) Suppose Michael cannot get the higher interest rate, nor increase his payments. How many months would he need to invest in order to achieve his goal?
Expert Solution
a) We can calculate the future value by using the following formula in excel:-
=fv(rate,nper,-pmt,fv)
Here,
FV = Future value
Rate = 12%/2 = 6% (semiannual)
Nper = 15*2 = 30 periods (semiannual)
Pmt = $1,000
PV = $0
Substituting the values in formula:
= fv(6%,30,-1000,0)
= $79,058.19
b) We can calculate the required rate by using the following formula in excel:-
=rate(nper,pmt,pv,-fv)
Here,
Rate = Required rate (semiannual)
Nper = 15*2 = 30 periods (semiannual)
Pmt = $1,000
PV = $0
FV = $120,000
Substituting the values in formula:
= rate(30,1000,0,-120000)
= 8.31%
Required rate = Rate * 2
= 8.31% * 2
= 16.63%
c) We can calculate the required payments by using the following formula in excel:-
=pmt(rate,nper,pv,-fv)
Here,
Pmt = Required payment
Rate = 12%/2 = 6% (semiannual)
Nper = 15*2 = 30 periods (semiannual)
PV = $0
FV = $120,000
Substituting the values in formula:
= pmt(6%,30,0,-120000)
= $1,517.87
d) We can calculate the number of payment periods by using the following formula in excel:-
=nper(rate,pmt,pv,-fv)
Here,
Nper = Number of payments period (semiannual)
Rate = 12%/2 = 6% (semiannual)
Pmt = $1,000
PV = $0
FV = $120,000
Substituting the values in formula:
= nper(6%,1000,0,-120000)
= 36.11 periods
Number of months = (Nper / 2) * 12
= (36.11 / 2) * 12
= 216.66 months
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