Question

Alex has decided to put away $11,687 in a bank account today, to save for his retirement.

His deposit is expected to earn an 3% p.a. rate of return, compounded monthly.
How much will alex have accumulated at the end of 36 years, when he retires?

Answer 1

Alex will have accumulated approximately $43,751.16 at the end of 36 years when he retires, given the initial deposit, interest rate, and compounding period.

Step-by-step explanation:

To calculate how much Alex will have at the end of 36 years, we can use the formula for compound interest:

A = P(1 + r/n)nt

Where:

• A is the final amount
• P is the initial deposit
• r is the annual interest rate (as a decimal)
• n is the number of times the interest is compounded per year
• t is the number of years

Plugging in the values from the question:

• P = $11,687
• r = 0.03 (3% as a decimal)
• n = 12 (compounded monthly)
• t = 36

We can now calculate:

1. Divide the annual interest rate by the number of times it is compounded per year: 0.03 / 12 = 0.0025
2. Calculate the number of times the interest is compounded over the given number of years: 12 x 36 = 432
3. Calculate the final amount: $11,687(1 + 0.0025)432 = $43,751.16

Therefore, Alex will have accumulated approximately $43,751.16 at the end of 36 years when he retires.