interest on internet saver

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  • ctweedie's Avatar
    Fresh Eyes
    Hey folks, I've just opened an internet saver account and I'm trying to figure out if I'll earn interest per month or just on the total balance at the end of the period? Im planning on saving more money each month in the account, and I'm not sure if I'd be better putting it elsewhere!
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  • ctweedie's Avatar
    Fresh Eyes
    I used chat gtp to help me understand, response below for anyone else that is confused!!
    You're absolutely right to question that! I made an error in how I explained the interest earned on the monthly deposits. Let's break it down carefully and correctly.

    How Interest Works on Monthly Deposits

    You save $100 each month, so after 12 months, you've saved a total of $1200. However, each monthly deposit will earn interest for a different amount of time, depending on when it was deposited.
    The key idea is that the monthly deposits will earn interest for varying periods — the first deposit will earn interest for 12 months, the second deposit for 11 months, and so on, until the last deposit earns interest for just 1 month.

    Correct Calculation of Interest on Monthly Deposits

    To get the correct interest earned on the monthly deposits, we will use the future value of a series of monthly deposits, considering monthly compounding.
    The formula for the future value of monthly deposits is:
    FV=P×((1+r/n)nt−1r/n)FV = P \times \left( \frac{(1 + r/n)^{nt} - 1}{r/n} \right) Where:

    • P=100P = 100 (monthly deposit),
    • r=0.042r = 0.042 (annual interest rate),
    • n=12n = 12 (compounding monthly),
    • t=1t = 1 year.

    Future Value of Monthly Deposits

    FV=100×((1+0.042/12)12−10.042/12)FV = 100 \times \left( \frac{(1 + 0.042/12)^{12} - 1}{0.042/12} \right) FV=100×((1+0.0035)12−10.0035)FV = 100 \times \left( \frac{(1 + 0.0035)^{12} - 1}{0.0035} \right) FV=100×(1.042685−10.0035)FV = 100 \times \left( \frac{1.042685 - 1}{0.0035} \right) FV=100×(0.0426850.0035)FV = 100 \times \left( \frac{0.042685}{0.0035} \right) FV=100×12.195=1219.50FV = 100 \times 12.195 = 1219.50 So, the future value of your monthly deposits (including interest) is $1219.50.
    This $1219.50 already includes both the $1200 you deposited and the interest earned on those deposits.

    Total Interest Earned on Monthly Deposits:

    • You deposited $1200 over the year, and the future value of those deposits (including interest) is $1219.50.
    • Therefore, the interest earned on the monthly deposits is:

    1219.50−1200=19.501219.50 - 1200 = 19.50

    Total Interest Earned for the Year:

    1. Interest on the initial deposit of $2400: $100.80
    2. Interest on monthly deposits (calculated above): $19.50

    Total Interest Earned:

    100.80+19.50=120.30100.80 + 19.50 = 120.30

    Final Balance After One Year:

    • Initial deposit: $2400 + $100.80 (interest) = $2500.80
    • Monthly deposits: $1200 + $19.50 (interest) = $1219.50

    Total balance at the end of the year:
    2500.80+1219.50=3720.302500.80 + 1219.50 = 3720.30

    Final Answer:

    At the end of the year, you will have $3720.30 in the account. This includes the initial $2400, the $1200 you saved over the year, and $120.30 in interest.

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