Question

What is the balance after 15 years in a savings account that earns 2% interest compounded bimonthly when the initial deposit is 1000?

Answer 1

$1348.07

Explanation:

Hello!

Compound Interest Formula:
`A = P(1 + \frac rn)^(nt)`

• A = Account Balance
• P = Principle/Initial Amount
• r = Rate of Interest (decimal)
• n = Number of times compounded (per year)
• t = Number of Years

Given Information

• Account Balance = ?
• Principle Amount = $1000
• Rate of Interest = 0.02

Why is the Rate 0.02?

This is because we are gaining money, so the multiplier should be greater than 1. We already added 1, which is 100% so you simply add the 0.02 for the extra 2%.

• Number of times compounded per year = 6

This is because it is being compounded bi-monthly, or once every 2 months. 12 months divided by 2 months is 6 months, so 6 times a year.

• Number of years = 15

Solve

Solve by plugging in the given values into the formula.

• 
  `A = P(1 + \frac rn)^(nt)`
• 
  `A = 1000(1 + \frac {0.02}{6})^(6*15)`
• 
  `A = 1000(1 + 0.00333...)^(90)`
• 
  `A = 1000(1.00333...)^(90)`
• 
  `A = 1000(1.145743)`
• 
  `A \approx 1457.43`

This is really close to the first option, and since there is rounding involved with the repeating decimal, the first option should be correct.

The answer is $1348.07.