Question

You want to have $300,000 when you retire in 30 years. If you can earn 4% interest compounded continuously, how much would you need to deposit now into the account to reach your retirement goal?

Answer 1

An amount of $ 92,495.60 must be the initial deposit to become into $ 300,000 by compound interest.

How much money must be deposited to  obtain a given quantity for retirement?

In this problem we must determine the initial deposit that must become into $ 300,000 by compound interest after a period of 30 years. Compound interest model is a model where money gains interest continuously, whose formula is:

C' = C · (1 + r / 100)ⁿ

Where:

• C - Initial deposit, in monetary units.
• C' - Final deposit, in monetary units.
• r - Interest rate, in percentage.
• n - Number of periods, in years.

If we know that C' = 300,000, r = 4 and n = 30, then the initial deposit is:

C = C' / (1 + r / 100)ⁿ

C = 300,000 / (1 + 4 / 100)³⁰

C = 92,495.60

The initial deposit must be $ 92,495.60.

To learn more on compound interest: https://brainly.com/question/13155407

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