My Not 2. Question Details TanFin12 5.2032 From age 25 to age 40, Jessica deposi

Question

My Not 2. Question Details TanFin12 5.2032 From age 25 to age 40, Jessica deposited $175 at the end of each month into a tax-free retirement account. She made no withdrawals or further contributions until age 65. Alex made monthly deposits of $300 into his tax-free retirement account from age 40 to 65. If both accounts earned interest at the rate of 4%/year compounded monthly, who ends up with the bigger nest egg upon reaching the age of 657 Hint: Use both the annuity formula and the compound interest formula. O Jessica Alex

Explanation / Answer

Here we will compare the final value of the amount paid by Jessica and Alex.

Here final value of the amount paid by Jessica. In the case of Jessica first we calculate Annuity paid by Jessica tll the year40 and then we will put compound interest on that value and get the final value amount at the year 65.

So final value at the age of 40 will be let say A40

here rate = 4/1200

time period = 15 years = 15 * 12 = 180 months

annuity = $ 175

A40 = 175 * [ (1 + 4/1200)180 -1]/ (4/1200) = $ 43065.8354

Here now we will put compound interest on that value

time period = 25 * 12 = 300 months

A65 = A40 * (1 + 4/1200)300 = 43065.8354 *  (1 + 4/1200)300 = $ 116870.5636

For ALex :

THe annuity amount when he will reach 65 years

P = $ 300

t = 25 * 12 = 300 years

r = 4/1200

A65 = 300 * [(1 + 4/1200)300 -1]/(4/1200) = $154238.8642

so , Alex will have more final value than the Jessica.

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