Question

A person who travels outside the country leaves a rental property for 5 years, with the condition that $4,500.00 per quarter is paid every end of the month, which will be deposited in a savings account that pays 8% compounded quarterly. What is the current value of the rental contract.

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Sigrid

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68 Answers

To find the current value of the rental contract, we need to calculate the future value of each quarterly payment and then sum them up.

First, let's calculate the future value of each quarterly payment using the compound interest formula:

A = P(1 + \frac{r}{n})^{nt}

Where:

A = future value

P = principal (quarterly payment)

r = annual interest rate (8% = 0.08)

n = number of compounding periods per year (quarterly = 4)

t = time in years

Let's substitute the given values into the formula:

A = 4500(1 + \frac{0.08}{4})^{4 \times 5}

Simplifying the exponent:

A = 4500(1 + 0.02)^{20}

Calculating the value inside the parentheses:

A = 4500(1.02)^{20}

Using a calculator or computer, we can find that:

(1.02)^{20} \approx 1.485947

Substituting this value back into the formula:

A \approx 4500 \times 1.485947

Calculating the result:

A \approx 6,686.26

Therefore, the current value of the rental contract is approximately $6,686.26.

First, let's calculate the future value of each quarterly payment using the compound interest formula:

Where:

A = future value

P = principal (quarterly payment)

r = annual interest rate (8% = 0.08)

n = number of compounding periods per year (quarterly = 4)

t = time in years

Let's substitute the given values into the formula:

Simplifying the exponent:

Calculating the value inside the parentheses:

Using a calculator or computer, we can find that:

Substituting this value back into the formula:

Calculating the result:

Therefore, the current value of the rental contract is approximately $6,686.26.

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