5.5: Exponential functions and investing

This is an equation that compounds interest throughout the years

What is S=P(1+r/k)^kt, dollars compounded throughout periods.

This is an equation that compounds the interest annually

What is S=P(1+r)^t

If $1000 dollars are invested at 5% interest compound annually for 7 years, what is the future value?

S= 1000(1+.05)^7=$1407.10

This is an equation that finds future value of investments when interest ‘r’ is compounded continuously

What is S=Pe^rt

If $1000 dollars is invested at 5% interest rate continuously for 7 years, what is the future value of investment?

S=1000e^(0.05)(7)=$1419.07

This is an equation that finds the present value of an investment

What is P= S(1+i)^-n

Find the future value of $10,000 placed in an account earning 8% per year for 10 years, interest is compounded: annually

k=1

• What is S=$10,000(1+0.08/1)^1 × 10

• s=$10,000 (1.08)^10

• =21,589.25

Find the future value of $10,000 placed in an account earning 8% per year for 10 years, interest is compounded: daily

k=365

• What is S=$10,000(1+0.08/1)^1 × 10

• S= $10,000(1.08)^10

• =$22,253.46

Between $22,253.46 and $21,589.25, what is the difference?

The difference is $664.21, which represents the additional value gained from daily compounding compared to annual compounding.