Ottawa Manor would like to buy some additional land and build a new assisted living center. The anticipated total cost is $12.4 million. The CEO of the ﬁrm is quite conservative and will only do this
When the company has suﬃcient funds to pay cash for the entire construction project. Management
Has decided to save $235,000 a month for this purpose. The ﬁrm earns 7% compounded monthly
On the funds it saves. How long does the company have to wait before expanding its operations?

Question

Quizplus · Accepted Answer

We need to find out how long it takes to save enough money to pay for the construction project, which costs $12.4 million.

We know that the company is saving $235,000 a month and earning 7% compounded monthly on those savings. The formula we can use to calculate the future value of an annuity is:

FV = PMT x [(1 + r)^n - 1] / r

Where:
FV = future value
PMT = monthly payment
r = interest rate per month
n = number of months

Plugging in the numbers we know:

FV = $12.4 million
PMT = $235,000
r = 0.07/12
n = ?

$12.4 million = $235,000 x [(1 + 0.07/12)^n - 1] / (0.07/12)

Solving for n:

n = ln[(12.4 million x 0.07/12) / (235,000 x 0.07/12 + 0.07/12)] / ln(1 + 0.07/12)

n = 46.14 months

Therefore, the company has to wait for 46.14 months before expanding its operations.

Ottawa Manor Would Like to Buy Some Additional Land and Build