Question

Rahul invested $1,100 in an account paying an interest rate of 3 3/8% compounded

quarterly. Caleb invested $1,100 in an account paying an interest rate of 3 1/4%
compounded daily. After 8 years, how much more money would Rahul have in his
account than Caleb, to the nearest dollar?

Answer 1

$13

Explanation:

You want to know how much more Rahul's investment of $1100 at 3 3/8% compounded quarterly for 8 years is worth than Caleb's investment of $1100 at 3 1/2% compounded daily for 8 years.

Rahul's account

The amount in Rahul's account is given by ...

A = P(1 +r/n)^(nt) . . . . . P invested at rate r compounded n times per year

A = $1100(1 +0.03375/4)^(4·8) = $1100(1.0084375^32) ≈ $1439.33

Caleb's account

The same formula is used for Caleb's account, but with different numbers.

A = $1100(1 +0.0325/365)^(365·8) ≈ $1426.61

Difference

The difference in account values is ...

Rahul's - Caleb's = $1439.33 -1426.61 = $12.72 ≈ $13

Rahul will have about $13 more in his account.

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