Exam 8: Compound Interest: Future Value and Present Value

What amount three years ago is equivalent to $4,800 on a date 1½ years from now if money earns 8% compounded semi-annually during the intervening time?

In order to pay off a debt that he took out today, Roger will have to make a payment of $3,500 in 15 months and $5,500 in 36 months. The interest rate is 8% compounded quarterly. What is the total amount of interest that is included in these payments?

A loan of $10,000 is being taken out today. The interest rate is 9% compounded monthly. Equal payments are to be made two and five years from now. After the second payment is made in five years there will be a balance of $3,000 still owing on the loan. Calculate the size of the two equal payments.

LottoNow offers a choice of $500 per week for 10 years or a lump sum payment of $220,000 now. If interest is 4.6% compounded semi-annually, determine which option should be chosen, and the economic difference between the two alternatives.

Mustafa can receive a $77.00 discount if he pays his property taxes early. Alternatively, he can pay the full amount of $2,250 when payment is due in 9 months. Which alternative is to his advantage if he can earn 6% compounded monthly on short-term investments? In current dollars, how much is the advantage?

Why is $100 received today worth more than $100 received at a future date? Is inflation the fundamental reason?

Calculate the missing value:

Krista invested $18,000 in a 3-year regular-interest GIC earning 4.2% compounded semi-annually. What is the semi-annual interest payment?

The quality control director at Ace Industries has determined that, currently far too many of the Aces they produce are defective. His target is to reduce the defective rate by 5% of the previous month's rate for each of the next six months. If he is successful what proportion of the current rate of defective Aces will he have eliminated?

Eric invested $22,000 in a 5-year regular-interest GIC earning 4.5% compounded monthly. What is each monthly interest payment?

Calculate the combined equivalent value of the scheduled payments on the indicated dates. The rate of return that money can earn is given in the fourth column. Assume that payments due in the past have not yet been made.

Liam borrowed $3,500 at 6.5% compounded monthly. After six months and one year, he paid $500 towards the outstanding balance. How much did Liam owe after three years?

Jacques has just been notified that the combined principal and interest on an amount he borrowed 19 months ago at 8.4% compounded monthly is now $2,297.78. How much of this amount is principal and how much is interest?

A two-payment stream consisting of $1,750 due today and $2,900 due in 18 months is to be replaced by an economically equivalent stream comprised of an undetermined payment due in 9 months and a payment of $3,000 due in 19 months. Calculate the unknown replacement payment if money is worth 4.2% compounded monthly.

Mrs. Janzen wishes to purchase 13 year-maturity strip bonds with $12,830 cash she now has in her RRSP. If these strip bonds are currently priced to yield 4.25% compounded semi-annually, how many $1,000 denomination bonds can she purchase?

Three years ago, Andrea loaned $2,000 to Heather. The principal with interest at 13% compounded semi-annually is to be repaid four years from the date of the loan. Eighteen months ago, Heather borrowed another $1,000 for 3½ years at 8% compounded semi-annually. Heather is now proposing to settle both debts with two equal payments to be made one and three years from now. What should the payments be if money now earns 6% compounded quarterly?

Payments of $2,000 due six months ago and $5,000 due three years from now, are to be replaced by two equal payments due now and one year from today. What is the amount of each payment if money is worth 12% compounded monthly? Use a focal date of today.

How much more will an investment of $10,000 be worth after 25 years if it earns 6% compounded annually instead of 5% compounded annually? Calculate the difference in dollars and as a percentage of the smaller maturity value.

How much interest is earned by investing $2100 for three years at 4.5% compounded monthly?

Michelle is reorganizing scheduled debt of $1,000 today and $2,000 due one year from now. It is to be settled by a payment of $1,500 three months from now and a final payment 18 months from now. If interest is 10% compounded quarterly, determine the size of the final payment.