First Trust offers personal loans at 7.7 percent compounded monthly. Second Bank
ID: 2733452 • Letter: F
Question
First Trust offers personal loans at 7.7 percent compounded monthly. Second Bank offers similar loans at 7.75 percent compounded semiannually. Which one of the following statements is correct concerning these loans?
The First Trust loan has an effective rate of 7.98 percent.
The Second Bank loan has an effective rate of 8.03 percent.
The annual percentage rate for the Second Bank loans is 7.90 percent.
Borrowers should prefer the loans offered by Second Bank.
First Trust offers the best deal on loans.
The First Trust loan has an effective rate of 7.98 percent.
The Second Bank loan has an effective rate of 8.03 percent.
The annual percentage rate for the Second Bank loans is 7.90 percent.
Borrowers should prefer the loans offered by Second Bank.
First Trust offers the best deal on loans.
Explanation / Answer
Loans from First Trust charged at an interset rate of 7.7% which is compounded monthly.
So monthly rate will be = Interest rate * Compounding period as a fraction of one year
=7.7%*1/12 =0.642% per month.
Loans from Second Bank charged at an interset rate of 7.75% which is compounded semiannually
So 6 Month rate will be = Interest rate * Compounding period as a fraction of one year
=7.7%*1/2 =3.85% per 6 Months.
For an example loan taken is $100000 for six month period,Loan at the end of Six months is
From First Trust = $100000*(1+0.00642)*(1+0.00642)*(1+0.00642)*(1+0.00642)*(1+0.00642)*(1+0.00642)
=$122725.92
From Second Bank=$100000*(1+0.0385) =$103850
Loan from first bank is $18875.92($122725.92-$103850) more than loan from second bank at the end of six month period.
so it is prefered to take loan from Second Bank at 7.75% compounded semi anuualy.
Borrowers should accept loans offered by Second Bank.
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