Finance time value of money

Question

Suppose you have $1.5 million loan with semi-annual installments over 10 years. How much do you pay towards the principal in the second installment if the interest rate of this loan is 1.8% compounded quarterly?

Answer 1

This problem is complicated by the fact that interest compounds quarterly, but the installment payments are semi-annual. We are not told how big the installments are. Based on quarterly compounding they should be $38,606.44 so we double that to make the semi-annual payment: $77,212.90

 

1. $1,500,000 x .018 x 3/12 = $6,750

2. 1,506,750 x .018 x 3/12 = $6,780.38

 

Payment: . . . . . $77,212.90

Less interest:  . . . .6,780.38

Principal paid: . .  70,482.52

 

Now the principal owed is $1,500,500 - 70,482.52 = 1,429,567.48. Now you can use this number to repeat the first two calculations above to find the principal paid in the second installment.