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Answer :
Final answer:
It would take Laurent approximately 67 months to save for the 20% down payment on the new condo units.
Explanation:
To calculate the time it would take Laurent to save for the 20% down payment on the new condo units, we can use the formula for compound interest. The formula is: A = P(1 + r/n)^(nt), where A is the future value of the investment, P is the principal amount (the initial investment), r is the annual interest rate (as a decimal), n is the number of times that interest is compounded per year, and t is the number of years. In this case, the principal amount is $132,000 and the future value we want to achieve is 20% of that, which is $26,400. The interest rate is 6.75% (or 0.0675 as a decimal), compounded monthly, and the monthly savings is $35. Plugging in these values, we get:
$26,400 = $132,000(1 + 0.0675/12)^(12t)
Simplifying the equation, we have:
5/24 = (1 + 0.0675/12)^(12t)
To solve for t, we need to take the logarithm of both sides of the equation. Using logarithmic properties, we can rewrite the equation as:
ln(5/24) = ln((1 + 0.0675/12)^(12t))
Using the power rule of logarithms, we can further simplify the equation:
ln(5/24) = 12t * ln(1 + 0.0675/12)
Now, we can isolate t by dividing both sides of the equation by 12 * ln(1 + 0.0675/12):
t = ln(5/24) / (12 * ln(1 + 0.0675/12))
Using a calculator, we can find that t is approximately 5.55 years. Since we want the answer in months, we multiply t by 12:
t (in months) = 5.55 * 12 = 66.6 months
Therefore, it would take Laurent approximately 67 months to save for the 20% down payment on the new condo units.
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