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

3.82 years

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

the answer to the question :

which best describes a central bank's primary goals? limiting inflation and reducing unemployment reducing unemployment and maintaining cash flow controlling stagflation and reducing unemployment managing credit and ensuring the money supply's liquidity

is:

managing credit and ensuring the money supply's liquidity