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

Answer:

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

Step-by-step 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

Answer:

The Unity Bank is offering a good plan.

Step-by-step explanation:

Unity Bank offers a monthly compounded interest rate of 0.14%

So, yearly rate will be = $0.14\times12=1.68$% 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.