Question

You are saving to buy a $185,000 house. There are two competing banks in your area, both offering certificates of deposit yielding 7 percent.
How long will it take your initial $102,000 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.)

Number of years

How long will it take your initial $102,000 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.)

Number of years

Answer 1

Answer:

(1) First Bank pay simple interest, number of year is 11.62 years

(2) Second Bank pay compound interest, number of year is 8.8 years

Explanation:

Future value (FV): $185,000

Rate: 7% per annual

Present value (PV): $102,000

Total interest required to have enough morning to buy a house = $185,000 - $102,000 = $83,000

(1) First Bank pay simple interest:

$83,000 = $102,000 * 7% * number of years

=> Number of years = $83,000/ ($102,000 * 7%)  = 11.62 years

(2) Second Bank pay compound interest:

$83,000 = $102,000*(1+7%)^number of years - $102,000

=> (1+7%)^number of years  = ($83,000+$102,000)/$102,000

⇔ (1.07)^number of years = 1.8137

=> Number of years = log (1.8137, 1.07) = 8.8 years