Question

Joe borrowed $8000 at a rate of 10.5%, compounded monthly. Assuming he makes no payments, how much will he owe after 9 years?Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

Given:

a.) Joe borrowed $8000 at a rate of 10.5%, compounded monthly.

For us to be able to determine how much will he owe after 9 years, we will be using the compounded interest formula:

`\text{ A = P\lparen1 + }\frac{\text{ r}}{\text{ n}})^(nt)^`

Where,

A=final amount

P=initial principal balance = $8,000

r =interest rate (in decimal form) = 10.5/100 = 0.105

n=number of times interest applied per time period = compounded monthly = 12

t=number of time periods elapsed (in years) = 9

We get,

`\text{ A = P\lparen1 + }\frac{\text{ r}}{\text{ n}})^(nt)`
`\text{ = \lparen8,000\rparen\lparen1 + }(0.105)/(12))^{12\text{ x 9}}\text{ = \lparen8,000\rparen\lparen1 + }0.00875)^(108)`
`\text{ = \lparen8,000\rparen\lparen1.00875\rparen}^(108)`
`\text{ = \lparen8,000\rparen\lparen2.49616052967\rparen}`
`\text{ A = 19,969.28423739091}`
`\text{ A }\approx\text{ \$19,969.28}`

Therefore, the answer is $19,969.28