## Your parents will retire in 30 years. They currently have \$350,000 saved, and they think they will need \$1,450,000 at retirement. What annua

Question

Your parents will retire in 30 years. They currently have \$350,000 saved, and they think they will need \$1,450,000 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.

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2 weeks 2021-09-12T21:36:47+00:00 2 Answers 0

1. Answer: the interest rate is 4.86%

Step-by-step explanation:

Assuming the interest was compounded annually, we would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = \$350000

A = \$1450000

n = 1 because it was compounded once in a year.

t = 30 years

Therefore,.

1450000 = 350000(1+r/1)^1 × 30

1450000/350000 = (1 + r)^30

4.14 = (1 + r)^30

Taking log of both sides of the equation, it becomes

Log 4.14 = 30 log(1 + r)

0.617 = 30 log (1 + r)

0.0206 = log(1 + r)

Taking exponent of both sides, it becomes

10^0.0206 = 10^log(1 + r)

1 + r = 1.0486

r = 1.0486 – 1 = 0.0486

Converting to percentage, it becomes

r = 0.0486 × 100 = 4.86%

4.85%

Step-by-step explanation:

1450000 = 350000(x³⁰)

x³⁰ = 4.1428571429

30lgx = lg4.1428571429

lgx = 0.0205766653

x = 10^0.0205766653

x = 1.0485198708

104.85%

So, interest is 4.85%