Final answer:
To find the value of a $1,000 deposit after two years with 6% interest compounded annually, use the formula A = P(1 + r/n)^(nt). After performing the calculations, the value of the amount will be $1,123.60.
Step-by-step explanation:
To calculate the future value of a $1,000 deposit in a savings account with a 6% interest rate compounded annually, we use the compound interest formula. This formula is A = P(1 + r/n)nt, where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
The problem specifies that the interest is compounded annually, which means n=1. We're looking to find the value after 2 years, so t=2. Also, our annual interest rate r is 6%, or 0.06 as a decimal.
The formula for our specific situation becomes:
A = $1,000(1 + 0.06/1)1*2 = $1,000(1 + 0.06)2
Performing the calculation step by step:
- Calculate the parentheses portion first: 1 + 0.06 = 1.06.
- Raise 1.06 to the power of 2: 1.062 = 1.1236.
- Multiply the principal amount by the result from step 2: $1,000 * 1.1236 = $1,123.60.
The account will be worth $1,123.60 at the end of the second year. The unit of measurement is US dollars (USD).