Question

Bruce and Lacey want to buy the condo they are currently renting. They have some money in a savings account, but the condo costs twice that much. If the account earns 4.13% interest compounded quarterly, how long will it take for their money to double?

Answer 1

It will take approximately 16.96 years for Bruce and Lacey's money to double in their savings account with a 4.13% interest rate compounded quarterly.

Step-by-step explanation:

To determine how long it will take for their money to double, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years. In this case, Bruce and Lacey have the principal amount in their savings account, which is half the cost of the condo. So, let's say their principal amount is P. The final amount they need to reach is 2P. The interest rate is 4.13% or 0.0413, and it is compounded quarterly, so n = 4. We need to solve for t.

Using the formula, we have: 2P = P(1 + 0.0413/4)^(4t)

Simplifying the equation further, we get: 2 = (1.010325)^(4t)

Using logarithms, we can solve for t:

log(2) = log(1.010325)^(4t)

log(2) = 4t * log(1.010325)

t = log(2) / (4 * log(1.010325))

Using a calculator, we find that t is approximately 16.96 years.