2. William and James are twin brothers aged 65. Thirty-five years ago (at the en
ID: 2808988 • Letter: 2
Question
2. William and James are twin brothers aged 65. Thirty-five years ago (at the end of the year when he reached age 30), William started an IRA (individual retirement account), putting $2,000 per year in the account at the end of each year. After 10 years of contributions, William stopped making new deposits but left the accumulated contributions in the IRA fund. The fund produced returns of 10 percent per year. No taxes are paid. James started his own IRA at the end of the year when he reached age 40 (25 years ago) and contributed $2,000 per year, making his last contribution today. Thus James invested 2 tines as much as william. James also earned 10 percent on his investments (tax free). (a) What are the values of Williams and James IRA funds today? (b) What personal finance lesson does this exercise suggest?Explanation / Answer
William IRA Fund :-
He Contributed $2,000 for 10 years and then didnt contribute capital from last 25 years.
So, in order to calculate its value at today, we will divide it in two parts, first we will find out its value at Age 40 till he was making contribution and then for remaining 25 years.
So using financial calculator, we will get :-
PV = 0, I/Y = 10%, PMT = 2,000, N= 10, Calculate FV = $31,874.85
Now, this is the amount at age 40 and then no conribution for 25 years but interest earned for 25years. So, we will get 31,874.85*1.10^25 = $345,354.63
James IRA Fund :-
Similar way we will calculate for James, he is contributing 2,000 for 25 years at 10% interest. Which means using Financial calculator :-
I/Y = 10% , N=25, PV= 0, PMT = 2,000. Calculate FV = 196,694.12.
So, this means William IRA Fund is value much higher than James, this teaches us the lesson, the earlier you start to save for your retirement, the better it is for you.
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