MATH SOLVE

3 months ago

Q:
# Skylar plans to use $3400 to open a savings account with an annual interest rate of 1.15%. How much more interest will he earn over 13 years if he chooses a compound interest account that compounds interest quarterly instead annually? Round your answer to the nearest cent.interest compounded annually: A = P (1 + r)tinterest compounded quarterly: A = P (1 +r/4)4t

Accepted Solution

A:

Answer:$ 2.5Step-by-step explanation:Given thatTotal Amount to be invested = P = $3400Total Time of investment = t = 13 yearsRate of interest = r = 1.15 %Lets calculate Simple interest firstAs we know formula for simple interest is[tex]A = P (1 +r)^{t} [/tex]Substituting the values[tex]A = 3400(1+ \frac{1.15}{100} )^{13}[/tex]A = $ 3944.9 Lets now calculate the compound interestAs we know formula for simple interest is[tex]A = P (1 + \frac{r}{n})^{nt}[/tex] As compound interest applies every 3 months so n =3So, [tex]A = 3400 (1 + \frac{1.15}{100*4} )^{13*4}[/tex] A = $ 3947.4Now Lets calculate how much more he will earn using compound interest.It can be found by taking difference of compound interest and simple interestAmount = 3947.4 - 3944.9 = $ 2.5 So Skyler must have earned 2.5 dollar more using the compound interest.