Question

Bob, proprietor of Bob's Burgers, would like to retire in 20 years. He plans to deposit $6500 at the end of each year for the next 20 years into an account expected to earn 7.5% compounded annually. How much will Bob have in his retirement account in 20 years immediately after making his last deposit

Answer 1

Answer:

$281,480

Explanation:

we need to find the future value of the annuity payments, we can use the future value of annuity formula (I couldn't find an annuity table for 7.5%):  

future value = annual payment x [(1 + r)ⁿ  - 1] / r

• annual payment = $6,500
• r = 7.5%
• n = 20 years

future value = $6,500 x [(1 + 0.075)²⁰ - 1] / 0.075 = $6,500 x 43.30468 = $281,480

Answer 2

The amount that Bob have in his retirement account in 20 years immediately after making his last deposit is $281,480.

Future value:

Using this formula

Future value =Annual payment x [(1 + Interest rate)^Number of years  - 1] / Interest rate

Where:

Annual payment = $6,500

Interest rate = 7.5% or 0.075

Number of years= 20 years

Let plug in the formula

Future value = $6,500 x [(1 + 0.075)²⁰ - 1] / 0.075

Future value=$6,500 x [(1 .075)²⁰ - 1] / 0.075

Future value=$6,500 x [(4.24785) - 1] / 0.075

Future value=$6,500 x [3.24785]/ 0.075

Future value = $6,500 x 43.30467

Future value= $281,480

Inconclusion the amount that Bob have in his retirement account in 20 years immediately after making his last deposit is $281,480.

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