GEMINI
Calculate the value of $7 per day for 10 years assuming a 4% interest rate per year
Okay, let’s figure out the future value of saving $7 per day for 10 years with a 4% annual interest rate. Since the contributions are made daily, we should consider the compounding effect more frequently than annually.
Here’s how we can approach this:
1. Calculate the total number of contributions:
* Number of years = 10
* Days per year = 365
* Total number of contributions = 10 \times 365 = 3650
2. Calculate the daily interest rate:
* Annual interest rate = 4% = 0.04
* Daily interest rate (approximately) = \frac{0.04}{365} \approx 0.000109589
3. Use the future value of an ordinary annuity formula:
Since the $7 is saved at the end of each day, this is an ordinary annuity. The formula for the future value of an ordinary annuity is:
FV = P \times \frac{(1 + r)^n - 1}{r}
Where:
* FV = Future Value
* P = Periodic Payment ($7)
* r = Interest rate per period (daily rate \approx 0.000109589)
* n = Total number of periods (3650)
4. Plug in the values and calculate:
FV = 7 \times \frac{(1 + 0.000109589)^{3650} - 1}{0.000109589}
FV = 7 \times \frac{(1.000109589)^{3650} - 1}{0.000109589}
FV \approx 7 \times \frac{1.491756 - 1}{0.000109589}
FV \approx 7 \times \frac{0.491756}{0.000109589}
FV \approx 7 \times 4487.28
FV \approx 31410.96
Therefore, saving $7 per day for 10 years at a 4% annual interest rate would result in approximately $31,410.96.
Very good ... A useful tool indeed ... How long did that take?
The problem seems to state simple interest (a 4% interest rate per year), while the AI response appears to solve for continuously compounded interest.