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How much money should be deposited today in an account that earns 3% compunded semiannually sonthat it will accumulate to $10,000 in three years

2 Answers

3 votes

Answer: 9,151

Explanation:

How much money should be deposited today in an account that earns 3% compunded semiannually-example-1
User Tomas Narros
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1 vote

Explanation:

To calculate how much money should be deposited today in an account that earns 3% compounded semiannually to accumulate $10,000 in three years, you can use the compound interest formula:

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

Where:

A = the future amount ($10,000 in this case)

P = the principal amount (the amount you want to find)

r = annual interest rate (3% or 0.03)

n = number of times interest is compounded per year (2 for semiannual)

t = the number of years (3 years)

You want to solve for P:

$10,000 = P(1 + 0.03/2)^(2 * 3)

$10,000 = P(1 + 0.015)^(6)

Now, simplify the equation:

$10,000 = P(1.015)^6

$10,000 = P(1.0931640625)

Now, divide both sides by 1.0931640625 to solve for P:

P = $10,000 / 1.0931640625

P ≈ $9,150.05

So, you should deposit approximately $9,150.05 today in the account to accumulate to $10,000 in three years when earning a 3% interest rate compounded semiannually.

User Bless
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