Question

Damon is saving up money for a down payment on a house. He currently has $4412, but knows he can get a loan at a lower interest rate if he can put down $5266. If he invests the $4412 in an account that earns 4.5% annually, compounded monthly, how long will it take Damon to accumulate the $5266

Answer 1

It will take approximately 3.591 years for Damon to accumulate $5266 and be able to get a loan at a lower interest rate for a down payment on a house.

Step-by-step explanation:

To calculate the amount of time it will take for Damon to accumulate $5266, you can use the formula for compound interest:

A=P(1+r/n)nt

In this formula, A is the future value, P is the present value, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, we have:

• P = $4412
• A = $5266
• r = 0.045 (4.5%)
• n = 12 (compounded monthly)
• t = ?

Plugging in these values, we can solve for t:

$5266 = $4412(1+0.045/12)12t

Dividing both sides by $4412:

1.192452 = (1+0.00375)12t

Taking the natural logarithm of both sides:

ln(1.192452) = 12t ln(1.00375)

Dividing both sides by 12 ln(1.00375):

t = ln(1.192452) / (12 ln(1.00375))

Using a calculator, we find that t is approximately 3.591 years.