SOLUTION: Kalil and Bob each invest $550 every 3 months into an account through their employer. The interest compounds quarterly, and Kalil's work offers him a rate of 5.6%/a whereas Bob’s

Question 1202559: Kalil and Bob each invest $550 every 3 months into an account through their employer. The interest compounds quarterly, and Kalil's work offers him a rate of 5.6%/a whereas Bob’s work offers him a rate of 5.2%/a.
a) How much will Kalil and Bob each have saved up in 6 years?
b) Who will earn more interest, and by how much?

Answer by math_tutor2020(3820) (Show Source): You can put this solution on YOUR website!

Answers:
(a) Kalil = $15,560.36 and Bob = $15,375.07
(b) Kalil earns $185.29 more.

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Work Shown for Part (a)

FV = future value
P = periodic deposit or payment
r = annual interest rate in decimal form
i = quarterly interest rate in decimal form
n = number of quarterly periods

1 quarter = 3 months

Future value of annuity formula

For Kalil we have
P = 550
r = 0.056
i = r/4 = 0.056/4 = 0.014 exactly
n = 6*4 = 24 quarterly periods

Compute the future value (FV) for Kalil

Kalil will have $15,560.36 saved up.

Bob's input value for P and n will be the same.
The key difference is that i = 0.052/4 = 0.013 exactly.

Compute the future value (FV) for Bob

Bob will have $15,375.07 in his account.

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Work Shown for Part (b)

Each person deposits $550 per quarter, for 24 quarters (aka 6 years).
Without interest that total deposit is 24*($550) = $13,200

Subtract this result from the results of part (a) to determine the interest earned.

Kalil = $15,560.36 - $13,200 = $2,360.36
Bob = $15,375.07 - $13,200 = $2,175.07

Kalil earned more interest. This is to be expected since Kalil's annual rate is larger compared to Bob's rate.
Both men have their money in their accounts for the same time frame, and same compounding frequency.

Subtract those results to see how big the gap is between the two.
Kalil - Bob = $2,360.36 - $2,175.07 = $185.29

Kalil earned $185.29 more dollars compared to Bob.

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