Question

Marley Woods Resort would like to buy some land and build a luxury living center. The anticipated total cost is $20.5 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 $1.2 million a quarter for this purpose. The firm earns 6.25 percent, compounded quarterly, on the funds it saves. How long does the company have to wait before expanding its operations

Answer 1

3.82 years

Step-by-step explanation:

FV of annuity = P[(1+r)^n - 1 / r]

Where FV = $20,500,000; P = $1,200,000; r = 6.25%/4 = 1.5625% quarterly

20,500,000 = 1,200,000 * [1+0.015625)^n - 1/0.015625]

20,500,000 / 1,200,000 = [1+0.015625)^n - 1/0.015625]

17.0833 = [(1+0.015625)^n - 1 / 0.015625]

17.0833 * 0.015625 = (1+0.015625)^n - 1

0.266927 = (1+0.015625)^n - 1

1.266927 = (1 + 0.015625)^n

Taking log of both sides of equation

LN(1.266927) = n*LN(1.015625)

n = LN(1.266927)/LN(1.015625)

n = 0.236594/0.015504

n = 15.26 quarters

No of years = 15.26/4

No of years = 3.82 years