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Chapter 5: Q. 28 (page 324)

Determine the rate that represents the better deal. 9% compounded quarterly or 914%compounded annually.

Short Answer

Expert verified

The answer is 9% compounded quarterly is a better deal.

Step by step solution

01

Step1. Given information

Let us first name A gives 9% compounded quarterly and B gives 914%compounded annually.

For A,

The rate of interest,r=9%=0.09

The investment compounded quarterly, n=4

For B,

The rate of interest, r=914%=374%=0.0925

The investment compounded annually, n=1

02

Step 2. Use effective rate of interest

The effective rate of interest rcof an investment earning an annual interest rate r compounding n times per year is given by,rc=1+rnn-1

03

Step 3. Calculation for A

Substitute the values of A in the effective rate of interest formula,

rc=1+0.0944-1rc=1.02254-1rc=1.09308-1rc=0.09308rc=9.308%

04

Step 4. Calculation for B

Substitute the values of B in the effective rate of interest formula,

rc=1+0.092511-1rc=1.0925-1rc=0.0925rc=9.25%

The effective rate of interest is highest for A, so 9% compounded quarterly is a better deal.

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