bank compounds

Question

Depostiting 3,000 for 6 years and 7 percent interest, what would be the return to the nearest cent?

 

 

What would be the return if the bank compounds monthly?

 

 

 

If compounds are continuous then formul used is A=pe(small n) where e is a constant and equals approximately 2.7183. Calculate A with continuious compounding. Round numbers to the nearest cent.

 

Answer 1

Your question is using the term "return" in an unusual way. Usually return refers to rate of return which in this case is the interest rate. For this problem, I will interpret return as the dollars earned as interest.

Also the formula you have for continuous compounding is not correct. A=P*e^(i*t) where A = Account value, P = initial balance, i = interest per year, and t = time in years. The symbol ^ means raised to the power of.

 

Let A(t) be the account value at time t in years.

Let r(t) = A(t)-3000

 

Annual compounding

 

A(6) = $3000*1.07^6=$4502.19

r(t) = $1502.19

 

Monthly compounding

 

A(6) = $3000*(1+.07/12)^(6*12) = $4560.32

r(t) = $1560.32

 

Continuous compounding

 

A(6) = $3000*e^(.07*6) =$4565.88

r(t) = $1565.88