glasskerfu

2020-10-23

Find the present value of the ordinary annuity.

If the amount of $500 of deposit in an account annually with an interest rate$9\mathrm{\%}$ per year for 25 years.

If the amount of $500 of deposit in an account annually with an interest rate

Laaibah Pitt

Skilled2020-10-24Added 98 answers

The present value of an annuity is calculated by the formula,

$PV=PMT\left(\frac{1\text{}-\text{}(1\text{}+\text{}i{)}^{-n}}{i}\right)$

Where PV is the present value

PMT is the amount of periodic payment i is the periodic interest rate,$i=\frac{r}{m}$

n is the total number of periods$n=mt$

r is the annual interest rate in decimals m number of compounding period per year.

Step 2

Here,

$PMT=\$500$

Compounded annually,$m=1$

Thus, the interest rate$i=r=0.09$ in decimals,

And the number of period$n=25$ years.

Substituting these values in the formula of the present value of an annuity,

$PV=500\left(\frac{1\text{}-\text{}(1\text{}+\text{}0.09{)}^{-25}}{0.09}\right)$

$=500\left(\frac{1\text{}-\text{}(1.09{)}^{-25}}{0.09}\right)$

$=4911.2898$

Rounding to the nearest cent,

$PV=4911.29$ dollars

Therefore, the present value of an annuity is $ 4911.29.

Where PV is the present value

PMT is the amount of periodic payment i is the periodic interest rate,

n is the total number of periods

r is the annual interest rate in decimals m number of compounding period per year.

Step 2

Here,

Compounded annually,

Thus, the interest rate

And the number of period

Substituting these values in the formula of the present value of an annuity,

Rounding to the nearest cent,

Therefore, the present value of an annuity is $ 4911.29.

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