Question

e the following situations to find when an account will reach a certain amount of money. (hint use your graphing, calculator) 21. You invest $1,000 at a fixed rate of 7% compounded monthly, when will your account reach $10,000? (round to the nearest year) 22. You purchase a house for $250,000 which increases in value every year at 4.5%. You plan to sell your house when it is worth $300,000. How many years will you have to live in the house? 23. Your parents start a college fund with $1500 that grows at 6.2% each year, when will the account reach $22,000 which will be the cost of your first 2 years of college?

Answer 1

1. Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value = $10000, PV = Present value = $1000, r = rate of interest = 7% compounded monthly, so monthly rate = 7% / 12 = 0.58333, n= time period

now, putting theses values in the above equation, we get,

$10000 = $1000 * (1 + 0.583333%)ⁿ

$10000 / $1000 = (1 + 0.0058333)ⁿ

10 = (1.00583333)ⁿ

(1.00583333)^40.62 = (1.00583333)ⁿ

n = 40.62

So, it will take 40.62 months or 40.62 / 12 = 3.38 or 3 years.

2. Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value = $300000, PV = Present value = $250000, r = rate of interest = 4.5%, n= time period

now, putting theses values in the above equation, we get,

$300000 = $250000 * (1 + 4.5%)ⁿ

$300000 / $250000 = (1 + 0.045)ⁿ

1.2 = (1.045)ⁿ

(1.045)^15.8 = (1.045)ⁿ

n = 15.8

So, we will have to live for 15.8 years.

3 Here we will use the following formula:

FV = PV * (1 + r%)ⁿ

where, FV = Future value = $22000, PV = Present value = $1500, r = rate of interest = 6.2%, n= time period

now, putting theses values in the above equation, we get,

$22000 = $1500 * (1 + 6.2%)ⁿ

$22000 = $1500 * (1 + 0.062)ⁿ

$22000 / $1500 = (1.062)ⁿ

14.6667 = (1.062)ⁿ

(1.062)^44.6 = (1.062)ⁿ

n = 44.6

So, it will take approx 44.6 years.