5) Frank funds his IRA, with 6.3% effective annual interest, at $1,000 per year

Question

5) Frank funds his IRA, with 6.3% effective annual interest, at $1,000 per year for 50 years. Gloria’s IRA account offers an interest rate of 5% compounded daily. A) How much cash is in Frank’s IRA after 50 years? B) What must Gloria’s annuity be for her IRA account balance to equal Frank’s after 50 years?  

6) John’s parents started a college fund earning 8% (compounded annually) on the day he was born in1990. They deposited $1,500 on his birthday each year until he turned 5, after that they began depositing $4,000 annually until he turned 18. When he was 16 he wanted to buy a car. Knowing that John’s college fund would need a balance of at least $100,000 when he started college, at the age of 18, how much did John’s parents allow him to withdraw from the fund to purchase his car?

7) The “We Dig It” Construction Company purchased an excavator (AKA “track hoe”) for $150,000 cash in 1998. They sold it this year (2018) for $15,000. Assuming that the depreciation on the track hoe was 3%, how much did “We Dig It” have to make each year to break even on the cost of the hoe? Assume that this money was in an account earning 5% interest. (Note, this does not include operation and maintenance costs,)

Explanation / Answer

As per policy only first question will be answered

5. Frank's IRA after 50 years = annuity *fvifa50, 6.3%

Fvifa =(1+r) ^n - 1 /r

Therefore,

Frank's IRA after 50 years =1000*(((1.063^50)-1)/0.063)=320888.67

Now to get same amount of 320888.67 at 5% compounded daily Gloria's annuity will be =320888.67/fvifa

=320888.67/(((1+(5%/365))^(50*365))-1)/(0.05/365))= 3.93

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