Question

Question:

How much money should be deposited today in an account that earns 2.5% compounded monthly so that it will accumulate to $10,000 in 3 years?

Answer:
The amount of money that should be deposited is ​$(blank)

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Answer 1

To accumulate $10,000 in 3 years in an account with a 2.5% interest rate compounded monthly, you need to deposit approximately $9284.95 today.

Step-by-step explanation:

To determine how much money should be deposited today in an account that earns 2.5% compounded monthly so that it will accumulate to $10,000 in 3 years, we use the formula for the present value of an investment compounded monthly:

`PV = FV / (1 + r/n)^(^n^t^)`

Where:

• PV is the present value (the initial amount to be deposited).
• FV is the future value ($10,000 in this case).
• r is the annual interest rate (2.5% or 0.025).
• n is the number of times interest is compounded per year (12 for monthly).
• t is the number of years (3 in this case).

First, we convert the interest rate from a percentage to a decimal by dividing by 100:

r = 2.5% / 100 = 0.025

Now we can calculate:

`PV = 10000 / (1 + 0.025/12)^(^1^2^*^3^)PV = 10000 / (1 + 0.00208333)^(^3^6^)PV = 10000 / (1.00208333)^3^6`

Therefore, the amount of money that should be deposited today is approximately $9284.95.