Question

you will create a scenario for investing money with compounding interest. the following formula models interest compounding continously.

Answer 1

Compounding interest

(CV) = PV x [1 + (i / n)]^{(n x t)}  

Where : CV= compounded value; PV= present value; i=interest rate in percentage; t=number of years; n=the number of compounding periods.

​​​​​​​Compounding continuously

The formula for continuously compounded interest is CV = PV x e ^{(i x t)}

Where, CV= compounded value; PV= present value; i=interest rate in percentage; t=number of years; e is approximated as 2.7183.

As an example, assume a $10,000 investment earns 15% interest over the next year in the mutual fund company. This will show the ending value of the investment when the interest is compounded annually, semiannually, quarterly, monthly, daily and continuously.

Thus, here PV=$10,000, i=15, t=1, n = the number of compounding periods.

When calculated by compounding interest method; CV= PV x e (i x t)

1. Annual Compounding: CV = $10,000 x (1 + (15% / 1)) ^{(1 x 1)} = $11,500
2. Semi-Annual Compounding: CV = $10,000 x (1 + (15% / 2)) ^{(2 x 1)} = $11,556.25
3. Quarterly Compounding: CV = $10,000 x (1 + (15% / 4)) ^{(4 x 1)} = $11,586.50
4. Monthly Compounding: CV = $10,000 x (1 + (15% / 12)) ^{(12 x 1)} = $11,607.55
5. Daily Compounding: CV = $10,000 x (1 + (15% / 365)) ^{(365 x 1)} = $11,617.98

Now, when compounded continuously method; CV= PV x e ^{(i x t)}

1. Continuous Compounding: CV = $10,000 x 2.7183 ^{(15% x 1)} = $11,618.34

Here we saw that, with daily compounding, the total interest earned is $1,617.98, while with continuous compounding the total interest earned is $1,618.34.