The formula to calculate the time required to save is:
\[ T = \frac{\log\left(\frac{P + \frac{M}{R}}{I + \frac{M}{R}}\right)}{\log(1 + R)} \]
where:
This calculator helps you determine how long you need to save to afford your dream item based on the price of the item, your monthly savings, the initial balance of your savings account, and the monthly interest rate.
Let's assume you are saving for a new car with a price tag of $33,000. You have an initial savings balance of $5,000, can save $1,500 monthly, and have a savings account with a monthly interest rate of 0.42%.
Step 1: Calculate the time required to save:
\[ T = \frac{\log\left(\frac{33000 + \frac{1500}{0.0042}}{5000 + \frac{1500}{0.0042}}\right)}{\log(1 + 0.0042)} \]
\[ T = \frac{\log\left(\frac{33000 + 357143}{5000 + 357143}\right)}{\log(1.0042)} \]
\[ T = \frac{\log\left(\frac{390143}{362143}\right)}{\log(1.0042)} \]
\[ T = \frac{\log(1.077)}{\log(1.0042)} = \frac{0.032}{0.0018} \approx 17.78 \text{ months} \]
You will be able to afford the new car after approximately 18 months, or 1.5 years.