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

(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

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