Final answer:
By the end of the 3rd year, with investments of $1,200, $2,000, and $3,400 at a 5% annual compounded interest rate, you will have $6,823.00 in your account when rounded to the nearest hundredth.
Step-by-step explanation:
To calculate how much you will have in your account by the end of the 3rd year with a series of investments at a 5.00% interest rate compounded annually, you need to calculate the future value of each separate investment at the end of year 3 and then sum them up.
- Investment at the end of year 1: $1,200 will compound for 2 years - FV = $1,200 × (1 + 0.05)2
- Investment at the end of year 2: $2,000 will compound for 1 year - FV = $2,000 × (1 + 0.05)1
- Investment at the end of year 3: $3,400 will compound for 0 years - FV = $3,400 × (1 + 0.05)0
To find the total, calculate each future value and add them together:
- FV for $1,200 investment: $1,200 × 1.1025 = $1,323
- FV for $2,000 investment: $2,000 × 1.05 = $2,100
- FV for $3,400 investment: $3,400 × 1 = $3,400
Total amount in the account by the end of year 3 = $1,323 + $2,100 + $3,400 = $6,823.
Rounded to the nearest hundredth, the total is $6,823.00.