Money, Banking, and International FinanceEquation 24 would have 240 terms. Consequently, mathematicians devised a formula to
calculate a mortgage with many payments.
For example, compute your monthly payment if you bought a $150,000 home at 6% APR
with a 30 - year mortgage. We calculated your monthly payment of $899.33 in Equation 25. If
you notice, Equation 25 is the same formula for an annuity payout with compounding frequency
included. Interest rate, i, is the APR interest rate divided by 12.
ܸܨ=
∙
ଵି(ଵା)ష∙=
.ହ∙ ,
ଵି(ଵା.ହ)షయబ∙భమ=$899.^33 (^25 )^
Amortization table can also handle balloon payments and variable interest rate mortgages.
However, these topics go beyond the textbook’s scope. A balloon payment is a person pays a
low monthly payment every month. For the last payment, the person would pay the remaining
balance, which could be large. Moreover, variable-interest rate loan is the bank can adjust the
loan’s interest rate as market interest rates change.
Foreign Investments
We can use the net present value (NPV) to calculate the monetary return to an investment
in Equation 26. This equation is almost identical to the present value formula, except the PV 0 is
negative and located on the right-hand side while we add a new variable, NPV. If the net present
value (NPV) equals zero, then this equation reduces to the present value formula. With the NPV
formula, we could invest the amount PV 0 today that generates the future cash flows, FVi, that
ends at Time T. Market interest rate is i, and it automatically compares out investment to the
market interest rate.
ܸܲܰ=−ܸܲ+
ிభ
(ଵା)భ+
ிమ
(ଵା)మ+⋯+
ி
(ଵା)^ (^26 )^
If we calculate a positive, net present value, then our investment is paying off.
Consequently, the investment is increasing the investor’s wealth because more money flows in
than out. Furthermore, investors would use the net present value formula to evaluate several
investment projects. Then they select the project with the highest NPV, as long as the NPV is
positive. An investor would never choose a project with a negative NPV because the project’s
return would be negative. Over time, more money flows out than in, creating a net loss.
For example, your brother wants you to invest $10,000 into his business. He promises to
repay you $12,000 in two years. If you invested your money into financial securities, you
believe you would earn an annual 10% APR. Is it profitable to invest in your brother’s business?
We calculated a net present value of - $82.64 in Equation 27. Unfortunately, you could earn
more on the financial securities than your brother’s business because the NPV is negative.