How is interest determined?
Simple Interest
•Elements that determine interest
expense/revenue: Principal, Interest rate, time
•Simple interest for one time period
–Interest = Principal * rate * time
–Future value = Principal + Interest
–Used to determine interest expense for
loans/investments usually less than a year with no
compounding
How is interest determined?
Compound Interest
•Compound interest-interest is earned not only on the
principal but also on the previous interest earned. Used
to determine interest when multiple years or periods.
–Future value = Principal * (1 + rate) * (1 + rate) *…
•In other words: Future Value = Principal * (1+rate)n
•Interest = Future Value less Principal
–Can solve the future value equation for Principal to answer
the question “How much do I need to invest today to have
$XX in the future.
•Present Value=Future Value/((1+rate)n
•(Principal = Present Value)
Single sum problems-Present Value
•What if we want to know the present value of an
amount that we’ll receive in the future?
•Or another way to put this same question-How
much do I need to invest today in order to have
$XX in the future?
–Present value of a single sum
–You need $75,000 to pay for a masters degree in 5
years. How much should you invest today assuming an
interest rate of 4% and interest is compounded
annually?
Single sum problems-Future Value
•What if we want to know what the future
value is of an amount we invest today?
–Future value of a single sum
–For example you invest an amount today, how
much will your investment be worth in 8 years?
–Invest $20,000 today @8% annual rate. How much
is your investment worth at the end of 3 years?
1. Interest is compounded annually.
2. What if interest is compounded semiannually?
Annuities
•Annuities are streams of payments that you pay or
you receive: Mortgage payments, car payments,
annuity payments you receive in retirement.
•Present value of a stream of payments
–How much should you invest today in order to receive
$5,000 at the end of the year for the next 8 years?
Assume an interest rate of 3%
•Future value of a stream of payments
–If you were to save $1,000 annually and earn 4%
interest, how much will you have in 5 years?
Annuities
•Present value of a stream of payments
–How much should you invest today in order to receive $50,000
at the end of the year for the next 20 years. Assume an interest
rate of 3%.
–We could present value each $50,000 payment….but there’s a
table for that (Present Value of an ordinary Annuity).
•Present value of an ordinary annuity (annuity paid/due at
the end of the period)
vs.
•Present value of an annuity due(annuity paid/due at the
beginning of the period). Won’t cover in this class!
