Question

# A year from now, you plan to begin saving for your retirement by making a deposit...

The total investment horizon is 30 years staring from today .

an total withdrawl horizon is 45 years on weekly basis.

At first we convert 7.5 % compounded montly to yearly APR .

EIR = (1+r/m)^m -1

or (1+ 0.075/12)^12 -1

or 7.763 % annualy is the rate we are going to use for calculations .

Now total number of withdrawls we have = 45 years x 52 weeks = 2340 withdrawls

Sum of withdrawl = \$200

I/Y weekly rate to be used = 7.763/52 = 0.1493% on weekly basis

So the target investment corpus is

200= Px0.001493/(1- (1+0.001493)^-2340

= \$129876.76 is the target investment .

Now we have to find the yearly deposits to meet the target.

FV = 129876.76

N = 30 years

Rate = 7.763 % on yearly basis

So we know

FV annuity = PMT x( (1+r)^n-1) / r)

PMT = FV / ((1+r)^n-1)/r

or

PMT = 129876.76 / ((1+0.07763)^30 -1 )/0.07763))

PMT = \$1197.30 per year

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