Simple Interest
The formula I = P * (r/100) * t
What is the name of this formula?
What Is Simple Interest?
Unlike simple interest, this type of interest earns interest on previously earned interest.
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 = P * (R/100) * t, 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 N?
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 return rate?
For long-term investments, this type of interest will almost always give a higher return
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
$1000 is invested at 6% compounded annually for 2 years. Calculate the future value.
What is $1123.60?
(A = 1000(1 + 0.06/1)^(1*2) = 1000(1.06)^2 = $1123.60)
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. This way of charging interest only on the initial amount borrowed hints at type of interest.
What Is Simple Interest?
You invest $2000 at a simple interest rate of 5% per year. This is how many years it will take to earn $300 in interest.
What is 3 years?
Explanation: I = P * (R/100) * t
$300 = $2000 * (5/100) * t
$300 = $2000 * 0.05 * t
$300 = $100 * t
t = $300 / $100 = 3 years
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?
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?
Initial is 100, with one year adding 5, and the second year you have $110.25.
($10.25 - $10 = $0.25 interest on the previous $5.)
You want to earn $200 in simple interest over 4 years from an account paying 2.5% annual interest. This is the principal you need to invest.
What is $2000.
(200 = P * 0.025 * 4 --> $200 = P * 0.10 --> P = $2000)
You invest $2000 at 4% interest compounded semi-annually for 5 years. Solve for the least amount of interest.
What is $437.99
A = 2000(1 + 0.04/2)^(2*5) = 2000(1.02)^10 = 2000 * 1.218994 = $2437.99
Interest = A - P = $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?
You are comparing two savings accounts. Account A offers 5% simple interest. Account B offers 4.8% interest compounded monthly. For a one-year investment, this account is better.
What is account A (simple interest)
Account A earns 5%
Account A (1 year): Earns 5% While Account B (1 year): A = P(1 + 0.048/12)^(12*1) = P(1.004)^12 ≈ P(1.04907).
Effective rate ~4.907%. Since 5% > 4.907%, Simple Interest is better for just one year.