Describe the difference between nominal, effective and real interest and calculate what is owed after 5 years for the following example. 10% interest on $100 over the course of 5 years. Where relevant, the compounding period is 1 year. Inflation is 5%.
The nominal interest rate is the stated interest of a given bond or loan. On the other hand, effective interest rate takes account of the compounding periods and financial costs. Nominal and effective interest rates are equal if they have the same compounding period. The difference is noticeable when the number of compounding periods increases. Another is the real interest which takes account of inflation rate. It is stated mathematically as the difference of the nominal interest rate and the inflation rate.
FW= $100 (F/P, .10, 5) = $100 (1.10)5 = $161.05. This is the amount owed after five years taking account of interest.
Taking account inflation rate, FW = $100 (1.10)5/ (1.05)5 = $126.19.
Calculate the simple interest applied to a loan with principal balance of $2,000 and a 7.3% interest rate after 16 years. Once you have the interest owed, give the total amount owed to pay off the loan.
Interest = Principal x number of periods x simple interest = $2,000 (16) (.073) = $2,336.00
Amount owed = Principal + interest = $(2,000 + 2,336) = $4,336.00
Upload an image of a graph that represents a balance with simple and compound interest. Time should be the x axis and the total balance should be the y axis. Units do not need to be labelled.
Figure 1: Balance for Simple and Compound Interest at 5% Interest and 100US$ Principal
Given an 8% effective interest rate, how much would you owe on a $15,000 loan after 2 years if it was compounded continuously?
r = nominal interest rate = ln (1+i) = ln (1.08) = 0.076961
F = Pern = $15,000 (e.076961(2)) = $17,496.00
If there is an inflation rate of 6.5% and a nominal rate of 9.3%, what is the real rate?
R= (N-I)/(1+I) = (.093-0.065)/(1.065) = 0.026291 = 2.63%
Calculate the present value of an investment if it will be worth $440,000 in 7 years with an annual interest rate of 3.5%.
PW = $440,000 (P/F, 0.035, 7) = $440,000/1.035^7 = $345,836.02
If a loan's principal was $290,000 and the amount paid after 5 years was $400,000, what was the nominal interest rate?
Compounding period is not stated. Thus nominal rate = effective rate.
$290,000 = $400,000/(1+i)5
Solve for i. nominal rate = effective rate = i = 0.066430 = 6.64%
You receive a $30,000 loan from a bank that must be paid off in 5 years. How much will you pay then if the loan has a nominal interest rate of 3% that is compounded daily?
Annual effective interest rate = i = (1+r/m)m-1 = (1+.03/365)365 -1 = 0.030453
FW= $30,000 (1.030453)5 = $34,854.81
If you invest $90,000 in a bond with nominal interest rate of 3%, how much profit will you make after 3 years?
Assume: Bond compounding period in semiannuals.
Annual effective interest rate = (1+.03/2)^2-1 = .030225
Profit = F – P = 90,000 (1.030225)^3 -90,000 = $8,409.89
Given the situation in question 9, what would the profit be if there is an inflation rate of 3.2% over the 3 years?
Profit = F – P = 89,536.41 – 90,000 = $-463.59.
This means that the investment is at a loss accounting inflation rate into the picture.