Isaw a new luminous green Yamaha RTV speed boat on my way home andbeing a speed boat fun decided to walk into the shop and inquireabout its price and payment plans that they offer for the boat. Whileinside the shop I found out that the boat was going for $ 10,000. Ialso found out they had an investment opportunity which promises tohave an average return of about 8% per year, compounded quarterly ifone invests long term. I need to know how much I need to invest for12 years to reach the $ 10,000 goal in time.
Thedesired item is Luminous Green Yamaha RTV speed boat
Thecost in 12 years will be about $ 10,000
Theaverage interest rate of the investment is 8%
Usingthe Present Value (PV) formula:
PVis the present value that amount to final value FV,iisinterest rate compounded quarterly and nyearsfor total payment.
Ihave divided one by the quantity raised to a power to remove thenegative sign on the exponent (–n). According to the rules ofexponents, this means that once the negative is put into effect, thebase quantity will change position by dropping down into thedenominator where it will be raised to the power of n. Then it willdivide FV instead of multiplying FV as it seems to be doing now.
n=48, because we have 48 quarters in the total 12 years (4quarters ina year). Because the time periods are for a period of three months,the discounting rate therefore becomes i= 2% (the rate accrued quarterly that result from the yearly rate of8% divided by four quarters annually).
CalculationUsing the PV Formula
Herethe relevant values are entered in the formula
Theinside parenthesis are added
Thenegative exponent creates the reciprocal of thebase number.
$3,865.35is the present value which i need to start investing, but having inmind that the interest rate will not remain the same for the 12years. I will start my investments with $4,000 this is to cover mefor inflation and such.
RequiredText: Dugopolski, M. (2012). Elementary and intermediate algebra (4thed.). New York, NY: McGraw-Hill Publishing.