What is the relationship between effective interest rate and compound interest?

3. Effective interest rate calculation

Effective Interest Rate Example 1:

Company ABC invests $100,000. The investment earns 12% per year compounded semiannually (i.e., two times per year).

EAR = (1 + 0.12 2)2 1 = 0.1236 or 12.36%

The EAR for this investment is 12.36% per year.

Effective Interest Rate Example 2:

Company ABC invests $100,000. The investment earns 12% per year compounded quarterly

(i.e., four times per year).

EAR = (1 + 0.12 4)4 1 = 0.1255 or 12.55%

The EAR for this investment is 12.55% per year.

We can see from these two examples that the effective interest rate increases as the frequency of compounding increases.

Effective Interest Rate Example 3:

Company ABC invests $10,000 at a nominal rate of 10%. Interest is compounded continuously. What will the investment be worth in two years? What is the EAR?

FV = $10,000 x (e0.10 x 2) = 10,000 x 1.2214 = $12,214

EAR = e0.10 x 2 1 = 1.2214 1 = 0.2214 or 22.14%

The EAR on this investment is 22.14%.

Effective Interest Rate Example 4:

Company ABC will receive $100,000 as a lump-sum payments in five years. The stated interest rate is 10%. Interest is compounded continuously. What is the present value of the future payment?

PV = $100,000 x (e-0.10x 5) = $100,000 x (0.60653) = $60,653

EAR = e0.10 x 5 1 = 0.6487

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