A student borrows $10 000 at an interest rate of 4% per annum, compounded monthly. a) If the student pays the loan off in 10 years, how much does the student pay in interest? # of compounding periods/year=12 total # of compounding periods = 12 x 10 = 120 Interest rate/compounding period = 4/12 = .33 Formula = 10,000 (1+1/300)^ ^ 120 or 1/3-in calc 1/300 = 14908 = 4,908 in interest was paid in interest (10,000 b) If the entire loan costs the student $20 000 to pay back, how many years was the loan for? 4908 20 000 10.000(1+1/3)^12N N=208.29 10 10,000 2) = (1+1/3+)^/QN 10g (2) = Log (1+1/3)²N 109 (2) 2210109 (1.3033) - -17.54 years 208.29 12 = 17.35 years.

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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I'm studying for my final and this question has me a bit confused. Although I got the answer I feel is right, why in the brackets do I multiply 10000 by (1+1/300) and not 1+1/3? I did both ways and couldn't get the right answer with multiplying by 1+1/3

A student borrows $10 000 at an interest rate of 4% per annum, compounded monthly.
a) If the student pays the loan off in 10 years, how much does the student pay in interest?
# of compounding periods/year = 12
total # of compounding periods = 12 x 10 = 120
Interest rate/compounding period = 4/12 = 33
Formula = 10,000 (1+1/300)^
^ 120
or1/3-in calc 1/300
= 14908 = 4,908 in interest was paid in interest. (10,000
4908)
b) If the entire loan costs the student $20 000 to pay back, how many years was the loan for?
20 000 = 10.000(1+1/3)^12N
N=208-29
10 000
10,000
2) = (1+1/3)^/QN.
10g/2) = Log (1+1/3) ²²
log (2) 2013109 (1.0033
ZIN
(11773
17.54 years
208.29
12
= 17.35
years
Transcribed Image Text:A student borrows $10 000 at an interest rate of 4% per annum, compounded monthly. a) If the student pays the loan off in 10 years, how much does the student pay in interest? # of compounding periods/year = 12 total # of compounding periods = 12 x 10 = 120 Interest rate/compounding period = 4/12 = 33 Formula = 10,000 (1+1/300)^ ^ 120 or1/3-in calc 1/300 = 14908 = 4,908 in interest was paid in interest. (10,000 4908) b) If the entire loan costs the student $20 000 to pay back, how many years was the loan for? 20 000 = 10.000(1+1/3)^12N N=208-29 10 000 10,000 2) = (1+1/3)^/QN. 10g/2) = Log (1+1/3) ²² log (2) 2013109 (1.0033 ZIN (11773 17.54 years 208.29 12 = 17.35 years
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