A $23,000 college loan with a rate of 4.76% compounded

he298c

he298c

Answered question

2021-08-16

A $23,000 college loan with a rate of 4.76% compounded quarterly is taken. After how many years will the taker owe $30,000 if making no payments?

Answer & Explanation

Brighton

Brighton

Skilled2021-08-17Added 103 answers

The formula for compounf interest:
A=P(1+rn)nt
Where:
P=principal=$23,000
r=interest rate (in decimal)=0.0476
n=amount of quarters in a year=4
A=the amount you owe=$30,000
t=amount of years=?
Substitute:
30,000=23,000(1+0.04764)4t
30,000=23,000(1+0.0119)4t
30,000=23,000(1.0119)4t
3023=1.01194t
log(3023)=log1.01194t
log(3023)=4tlog1.0119
log(3023)4log1.0119=t
t22.5
Answer: after 22.5 years

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