Simple Interest
The formula I = C x r x n
What is the name of this formula?
What Is Simple Interest?
(C = capital, r = interest rate, n = number of periods, I = interest)
This interest is added to the original amount and the new value is used to calculate the interest for the next period.
What Is Compound Interest?
On a finance app (like a TI-84 TVM Solver), this input stands for the Present Value.
What is PV?
The original sum of money borrowed or invested
What is principal/initial?
This type of interest is calculated only on the initial amount.
What is simple interest?
I = C x r x n, this letter represents the annual interest rate as a percentage number (e.g., 5 for 5%).
What is r?
In a TVM solver, this letter represents the number of times interest is compounded per year.
What is CY / PY?
If you are calculating a 5-year investment compounded monthly, what value will you enter for N?
What is 60? (5x12 months)
The cost of borrowing money or the return on an investment, usually expressed as a percentage.
What is interest rate/rate of return?
For long-term investments, this type of interest will almost always give a higher return
What Is Compound Interest
You invest $500 at 4% simple interest for 3 years. This is the amount earned.
What is $60?
I = 500 * (4/100) * 3 = 500 * 0.04 * 3 = $60
The more frequently interest is compounded (e.g., monthly vs. annually), this is the effect on the total amount earned.
What is earning more interest?
If you invest $500 (an outflow from you), this value for PV is typically entered as negative on the TVM Solver.
What is -500?
The total value of an investment at a specific point in the future.
What is future value?
You lend a friend $100 and they agree to pay you back the $100 plus an extra $5 in interest at the end of each month. If they don't, they owe you another $5 on top of the original $100. What type of interest is this?
Simple Interest
Sarah invests $2,000 (C) in a savings account that offers a simple interest rate of 3% per year (r). If she leaves the money in the account for 4 years (n), how much interest (I) will she earn?
$240 in interest after 4 years.
Explanation:
I = 2,000 x 0.03 x 4 = 60 x 4 = 240.
I = Interest earned
C = Principal amount = $2,000
r = Annual interest rate = 3% = 0.03 (Remember to convert the percentage to a decimal)
n = Number of years (period) = 4 years
$1000 is invested at 6% compounded annually for 2 years. Calculate the future value.
What is $1123.60?
Explanation:
PV = 1,000
r = 0.06.
n =2
k = 1 (compounded annually)
---
FV = 1000 x (1 + 6 / (100))^(2)
FV = 1000 x (1.06)^2
FV = 1000 x 1.1236
FV = 1123.60
For an investment where you deposit a lump sum and make no further payments, this TVM Solver input is set to 0.
What is PMT?
The potential for an investment to generate a lower-than-expected or negative return; generally, higher potential returns come with this being higher.
What is risk?
You put $100 in a savings account. After year 1, you have $105, after two years you have $110.25. This type of interest is being used.
What Is Compound Interest?
Simple interest would earn $5 each year (5% of the original $100). So after 2 years, you'd have $100 + $5 + $5 = $110, and a total interest of $10.
With compound interest, you earned a total of $110.25 - $100 = $10.25 in interest.
You want to earn $200 in simple interest (I) over a period of 4 years (n). If the account pays an annual simple interest rate of 2.5% (r), what is the principal amount (C) you need to invest?
What is $2000.
C = $200 / 0.10 --> (0.025 x 4) interest rate & period.
This equals out to $2,000.
You invest an initial amount of $2000 (PV) for 5 years (n). The investment earns a nominal annual interest rate of 4% (r), and the interest is compounded semi-annually (meaning the number of compounding periods per year, k, is 2).
What is $437.99
FV = 2000 x (1 + 4 / (100 x 2))^(2 x 5)
FV = 2000 x (1 + 4 / 200)^(10)
FV = 2000 x (1.02)^10
(1.02)^10 ≈ 1.2189..
FV = 2000 x 1.2189..
FV ≈ 2437.9888...
FV ≈ $2437.99 (rounded to two decimal places)
Interest = FV - PV = $2437.99 - $2000 = $437.99
Your inputs are: N=36, I%=5, PV=-1000, PMT=0, P/Y=12, C/Y=12.
Considering the options, you would solve for this.
What is FV? ($1,161.47)
This percentage rate reflects the actual annual rate of return taking into account the effect of compounding interest. It's what you use to truly compare accounts with different compounding frequencies.
What is annual percentage yield?
You are evaluating two long-term investment options for a principal amount, P, over a 10-year period.
Option A: Offers a 4.5% simple annual interest rate.
Option B: Offers a nominal annual interest rate of 4.2% (r), but this interest is compounded quarterly (k=4).
What is account B.
Option A only gives a FV of 1.45.
(100 + 4.5%)
Option B gives a FV of 1.51.
P x (1 + 4.2 / (100 x 4))^(4 x 10)
(1.0105)^40 = 1.51.