undin g your et ement raonal nance Pro c Yo plan to e reinanacty 21 y cars Your
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undin g your et ement raonal nance Pro c Yo plan to e reinanacty 21 y cars Your god kto crestc and ha aloe you o ec ve S2 at he do co h et rthc 3 ycars bct c n cres tand de th psychic told youthat you woulddecka bycarsa er you tre. You n that you be c. Whan efact wold an Inceasin a rata you can cam bath dring and prior to ratinamant hae on tha valus tound In parts aand b Elain d. Now 55ume the vo w earr 0% rom now through he end of our retirement You ant oo make 21, end sear eposits m o our re ren en accou t that fund he year stes m o 521.000 annus annuly payments How Irge your annual deposits have to be? a. The amount of the fund you wilnced wien you retve in 21 years to provide th 3-year, $21,000 retirement annuity is b. The amount you » need toder as 5ande amour t to provide the und calculated n part Vou ear on y 9% per year dunng the 21 veers preceangrerement is $ Round to the nearest cent. c. What offect would an increa in thrt you can cam bath during and pricr to retirement hae on the valus found in par and b?(Sclect from the crop dawn menus.) In the calculation or present values you should notce that the nghar te intarest rate, the lower the present value Therefore In pat and b both values would be | n other words eamount wouishave tobe ut aaytoy sum would be neaded In 21 years for the annuity and a amount would hae to be pt away tccay to accumu ate the " you want to maka 21 andat aar deposits into your re remant account tat wil tund tha2s sar stream or S21 D00 annual ann ty pa marts, your annual da Sts ·ba S Ha nd to t a narast cantExplanation / Answer
a.
We can use formula for PV of annuity to compute required fund size at the time of retirement as:
Formula for PV of annuity is:
PV = P x [1-(1+r)-n/r]
P = Periodic retirement cash flow = $ 21,000
r = Rate per period = 11 % or 0.11 p.a.
n = Numbers of periods = 35
PV = $ 21,000 x [1-(1 + 0.11)-35/ 0.11]
= $ 21,000 x [1-(1.11)-35/ 0.11]
= $ 21,000 x [(1-0.025923626)/ 0.11]
= $ 21,000 x (0.974076374/ 0.11)
= $ 21,000 x 8.8552398
= $ 185,960.04
$ 185,960.04 of fund is needed at the time of retirement.
b.
The single amount needed to invest today can be computed as:
PV = FV/ (1+r)n
PV = Present value of retirement fund
FV = Fund size after 21 years = $ 185,960.04
r = Rate per period = 9 % or 0.09 p.a.
n = Numbers of periods = 21
PV = $ 185,960.04/ (1+0.09)21
= $ 185,960.04/ (1.09)21
= $ 185,960.04/ 6.108807737
= $ 30,441.30
c.
If interest rate is increased,
In part a and b both values would be less. In other word a less sum would be needed in 21 years for the annuity and a less amount would have to put away today to accumulate the needed future sum.
d.
If r = 10 % pr 0.10 p.a. PV will be:
PV = $ 185,960.04/ (1+0.1)21
= $ 185,960.04/ (1.1)21
= $ 185,960.04/ 7.400249944
= $ 25,128.89
$ 25,128.89 of fund is required for retirement, if interest rate increase to 10 %.
If deposited annually, annual saving amounts can be computed using formula for FV of annuity as:
FV = P x [(1+r) n – 1/r]
P = FV/ [(1+r) n – 1/r]
FV = Future value of annuity = $ 185,960.04
P = Periodic cash savings
r = Rate per period = 10 % or 0.10 p.a.
n = Numbers of periods = 21
P = $ 185,960.04/ [(1+0.1)21 – 1/0.1]
= $ 185,960.04/ [(1.1)21 – 1/0.1]
= $ 185,960.04/ [(7.400249944 – 1)/ 0.1]
= $ 185,960.04/ (6.400249944/0.075)
= $ 185,960.04/64.00249944
= $ 2,905.51
$ 2,905.51 need to deposit annually for 21 years at discount rate of 10 % to achieve the desire goal.
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