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Andreyy89
3 years ago
11

Your parents will retire in 29 years. They currently have $200,000 saved, and they think they will need $2,400,000 at retirement

. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places.
Business
1 answer:
zhannawk [14.2K]3 years ago
3 0

Answer:

8.95%

Explanation:

Data provided in the question:

Time, n = 29 years

Principle amount = $200,000

Future value = $2,400,000

Now,

Using the compounding formula

Future value = Principle × [ 1 + r ]ⁿ

here,

r is the interest rate

Thus,

$2,400,000 = $200,000 × [ 1 + r ]²⁹

or

[ 1 + r ]²⁹ = 12

taking the natural log both the sides, we have

29 × ln(1 + r) = ln(12)

or

ln(1 + r) = 0.08569

or

1 + r = e^{0.08569}

or

1 + r = 1.0895

or

r = 0.0895

or

r = 0.0895 × 100% = 8.95%

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