an apartment for $900 a month, rent will increase by 5.5% each year, how much will the rent be in 7 years

Question

Please show me how to do this, and if there a formula for this. 

Answer 1

This problem is similar to a compound interest problem.

Listing the amount of rent by year, you can check your answer at the end (Note: Due to rounding, the answers might not be exactly equal).

Year 1: $900

Year 2: $900 + ($900*.055)= $949.50

Year 3: $949.50 + (949.50*.055)= $1001.72

Year 4: $1001.72 + (1001.72*.055) = $1056.81

Year 5: $1056.81 + (1056.81*.055) = $1114.93

Year 6: $1114.93 + ($1114.93*.055) = $1176.25

Year 7: $1176.25 + ($1176.25*.055) = $1240.94

Year 8(after 7 years): $1240.94 + (1240.94*.055) = $1309.19

 

The formula for compound interest is:

S = P(1 + (j/n))^nt

Where S is the total amount of principal and interest. P is the principal amount(starting amount). j is the interest rate, and n is the number of times interest is compounded each year. t is the number of years.

Substituting the known values:

S = $900(1 + (.055/1))⁽¹⁾⁽⁷⁾

S = $900(1 + .055)⁷

S = $900(1.055)⁷

S = $900(1.45467918)

S = $1309.21

Answer 2

To do growth rate problems, you do the following:

 

1. Add 1 to the growth rate per unit of time (years, in this case)

2. Take the result to the power of the number of units  (years)

3. Multiply by the starting value

 

So the formula is

 

V = A (1+r)ⁿ

 

V is the final value

A is the starting value

r is the growth rate per period (as a decimal -- if they give it as a percentage you have to divide by 100)

n is the number of periods

 

So in this case it would be 900 * 1.055⁷, which you can work out on a calculator.