Question

Samir is trying to decide between two checking account plans. After researching plans at two banks, he finds that Unity Bank offers a monthly compounded interest rate of 0.14%, while Sunrise Banking offers 1.6% interest compounded annually. Which is the better plan? Explain.

(SHOW WORK)

Answer 1

The monthly compounded interest rate of 0.14% of Unity Bank is a better plan.

Explanation:

Step 1 : Write the formula for calculating a monthly compound interest rate and for calculating an annually compounded interest rate.

Monthly compound interest rate = P(1+r/n)^nxt

n=12 (number of months in a year)

t=1 (number of years)

Annually compound interest rate = P(1+r/n)^nxt

n=1 (because it is for 1 year only)

t=1 (number of years=1)

Step 2 : Lets assume that P is $100 in both banks and time is 1 year.

Step 3 : Lets substitute the values to find out which one is better.

Monthly compound interest rate = P(1+r/n)^nxt

Monthly compound interest rate = 100(1+0.14/12)^12x1

Monthly compound interest rate = 114.93

114.93 - 100 = $14.93 per month

14.93 x 12 = $179.16 for 12 months or 1 year

Annually compound interest rate = P(1+r/n)^nxt

Annually compound interest rate = 100(1+1.6/1)^1x1

Annually compound interest rate = 260

260-100 = $160 for 1 year

Therefore, the monthly compounded interest rate of 0.14% of Unity Bank is a better plan.

!!

Answer 2

The Unity Bank is offering a good plan.

Explanation:

Unity Bank offers a monthly compounded interest rate of 0.14%

So, yearly rate will be =
`0.14*12=1.68`% or 0.0168

Sunrise Banking offers 1.6% or 0.016 interest compounded annually.

Lets check an example with these two rates.

The compound interest formula is =
`A=P(1+r/n)^(nt)`

Lets take P = $1000 and t = 1 year

Case 1: when r = 1.68% and n = 12

Putting the values in formula we get

A =
`1000(1+0.0168/12)^(12)`

=
`1000(1.0014)^(12)`

A = $1016.92

Case 2: when r = 1.6% and n = 1

Putting the values in formula we get

A =
`1000(1+0.016/1)^(1)`

=
`1000(1.016)^(1)`

A = $1016.00

So, we can see that the first case gives more return than second one.

Therefore, the Unity Bank is offering a good plan.