Question

draw a timeline, show the formula, and include your calculator inputs.

Kevin is 35 years old, and has decided to wait until his 36th birthday to start saving money for retirement. He plans to save $2,500 a year beginning at age 36 and continue until he is 65 years old (30 years). (Draw a timeline for this problem and treat as an ordinary annuity.) How much will Kevin have when he is 65 years old, assuming he will earn an average rate of 6%?

Answer 1

Accumulated value = $209504.19

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Total deposits made = 30

The future value of annuity due formula is used to calculate the ending value of a series of payments or cash flows where the first payment is received immediately. The first cash flow received immediately is what distinguishes an annuity due from an ordinary annuity.

FV of annuity due = (1 + i) * P [{(1 + i) ^n -1}/i]

Where,

Periodic deposit (P) = $2500

Interest rate = 0.06

Time (n) = 30

Let's put all the values in the formula to solve for FV of annuity due

FV of annuity due = (1 + 0.06) * 2500 [{(1 + 0.06) ^30- 1}/ 0.06]

= (1.06) * 2500 [{(1.06) ^30- 1}/ 0.06]

= 2650 *[5.74349117291326- 1/ 0.06]

= 2650 *[4.74349117291326/ 0.06]

= 2650 * 79.058186215221

= 209504.19

So FV of annuity due is $209504.19

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