A) Suppose at age 25, you decide to save for retirement by depositing $95 at the

Question

A) Suppose at age 25, you decide to save for retirement by depositing $95 at the end of every month in an IRA that pays 4.25% compounded monthly. How much will you have from the IRA when you retire at age 65? Determine the interest. Round to the nearest dollar.

B) How much should you deposit at the end of each month into an IRA that pays 6.5% compounded monthly to have $4 million when you retire in 45 years? How much of the $4 million comes from interest? (invest early in your career, let interest work for you)

Explanation / Answer

The future value of the IRA (individual retirement account) is given by the formula F = P[(1+r)n-1]/r where P is the periodic payment, r is the rate per period, n is the number of periods and F is the maturity value of the IRA. Here, P = $ 95, r = (4.25/100)*1/12 = 425/120000=17/2800 and n = (65-25)*12 = 480.

Then, we have

F = 95[ (1+17/2800)480 -1]/( 17/2800) =$ 270285.90

The amount deposited in 40 years ( between 25 and 65) is $ 95*40*12 = $ 45600

Therefore, the amount of interest is $ 270285.90- $ 45600 = $ 224685.90

1.The amount from IRA on maturity will be $ 270285.90

2.The amount of interest is $ 224685.90.

2).

Future Value of Ordinary Annuity = P*{(1+r)^n-1)}/r

r= 6.5% or 0.54 % Per Months

n= 45 Yrs or 540 Months

Present Value of Anniuty = 40,00,000

4000000=P*{((1+0.0054)^540-1)}/0.0054

P = $ 1250.44

Interest is = 4000000- (540*1250.44)

= $3324762.4

r= 6.5% or 0.54 % Per Months

n= 45 Yrs or 540 Months

Present Value of Anniuty = 40,00,000

4000000=P*{((1+0.0054)^540-1)}/0.0054

P = $ 1250.44

Interest is = 4000000- (540*1250.44)

= $3324762.4

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