Exponential Functions and Logarithms

Question

1. Fred inherited $35,000 from his uncle. He decides to invest his money for 5 years in order to have the greatest down-payment when he buys a house. He can choose from 3 different banks.
Bank A offers 1% compounded monthly.
Bank B offers .5% compounded continuously.
Bank C offers .75% compounded daily.

Which bank offers the best plan so Fred can earn the most money from his investment?

Answer 1

For the monthly and daily banks, the formula is"

 

P(5) = ($35,000)(1 + r/n)^nt

• P(5) = principle in 5 years
• r = rate expressed as a decimal (note 0.75% = 0.0075)
• n = number of compoundings per year, 12 for monthly and 365 for daily
• t = time = 5 years

 

Plug in the numbers and use your calculator to get the answer.  For the continuous compounding, the formula is:

 

P(5) = ($35,000)e^rt

• e = euler's number (it's on your calculator)
• r = rate expressed as a decimal = 0.5% = 0.005
• t= time = 5 years.

 

Plug in the numbers and compute the answer with your calculator.