You borrowed $1,500 at 6% compounded annually. your payments are $90 at the end of each year. how many years will you make payments on the loan?

Given the formula for future value annuity:

FV of annuity=P[ (1+r) ^n-1]/r

where:

P=principle

r=rate

n=time

the time taken to repay the loan will be:

1500=90[ (1+0.06) ^n-1]/0.06

90=90[ (1+0.06) ^n-1]

1 = (1+0.06) ^n-1

1+1 = (1+0.06) ^n

2=1.06^n

introduce natural log

ln2=nln1.06

n=ln2/ln1.06

n=11.8957=12 years

the answer is 12 years.