Question

You are saving to buy a $181,000 house. There are two competing banks in your area, both offering certificates of deposit yielding 6.6 percent. a. How long will it take your initial $98,000 investment to reach the desired level at First Bank, which pays simple interest? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. How long will it take your initial $98,000 investment to reach the desired level at Second Bank, which compounds interest monthly? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

a) 12.83 years

b) 9.32 years

Explanation:

a) 181000-98000/(98000*6.6) = 12.83 years

b) FV=PV(1+rate)^time

   time=111.86

   years=111.86/12=9.32 years

Answer 2

Answer:

Solution 1:

Simple Interest = Principle × Rate × Time

Time = Simple Interest / Principle × Rate

Presently, all together for introductory venture of $98,000 to reach $181,000 = $83,000 of premium should be earned  

$83,000 = $98,000 * 6.6% * n  

n = 12.83 years  

Solution 2:  

For self multiplying dividends,  

$Future Value = Present Value(1 + r)^{n}$

Presently the aggravating occurs on month to month premise,

So,

r = 6.6% / 12

r = 0.55% (Monthly);  

$181,000 = 98,000 (1 + 0.55%)^{n}$  

$1.8469 = 1.0055^{n}$

Taking log of the two sides,  

LN(1.8469) = n * LN(1.0055)  

0.6135 = n * 0.005485  

n = 111.86 months  

n = 111.86/12

n = 9.32 years