Chapter 4, Problem 89P

(a)

To determine

Monthly interest rate.

Answer to Problem 89P

Monthly Interest rate is 0.98%.

Explanation of Solution

Given information:

Loan amount: $1,000

Duration: 12 Months

Amount of monthly payment is $ 93.12.

Loan amount is $1,000, Amount of monthly payment is $93.12 and Duration is12 Months.

$\begin{array}{l}\text{Total Amount Repaid = Amount of monthly payment of \$ 93}\text{.12 x Duration of 12 Months}\hfill \\ \begin{array}{l}\\ \text{Total Amount Repaid = \$1,117}\text{.44}\end{array}\hfill \\ \begin{array}{l}\\ \text{Less: Loan Amount = \$1,000}\end{array}\hfill \\ \begin{array}{l}\\ \text{Interest Paid for 1 Year = \$117}\text{.44}\end{array}\hfill \\ \begin{array}{l}\\ \text{Rate of interest per month = Interest Paid for 1 Year / Loan Amount / 12}\end{array}\hfill \\ \hfill \\ \text{Rate of interest per month = 0}\text{.9787\%}\hfill \end{array}$.

Conclusion:

Hence the monthly interest rate is calculated.

(b)

To determine

Nominal annual interest rate.

Answer to Problem 89P

Nominal annual interest rate is 11.744%.

Explanation of Solution

Given information:

Loan amount : $1,000

Duration: 12 Months

Amount of monthly payment is $ 93.12.

Loan amount is $1,000, Amount of monthly payment is $ 93.12 and Duration is12 Months.

Nominal annual interest rate is calculated as periodic interest rate expressed in terms of a year. For instance, a periodic monthly interest rate is expressed in terms of a year by multiplying the same by 12.

Interest rate per month is calculated at 0.98% per month. Hence the annual interest rate is calculated as Monthly interest rate multiplied by 12.

$\begin{array}{l}\text{Total Amount Repaid = Amount of monthly payment of \$ 93}\text{.12 x Duration of 12 Months}\hfill \\ \begin{array}{l}\\ \text{Total Amount Repaid = \$1,117}\text{.44}\end{array}\hfill \\ \begin{array}{l}\\ \text{Less: Loan Amount = \$1,000}\end{array}\hfill \\ \begin{array}{l}\\ \text{Interest Paid for 1 Year = \$117}\text{.44}\end{array}\hfill \\ \begin{array}{l}\\ \text{Rate of interest per month = Interest Paid for 1 Year / Loan Amount / 12}\end{array}\hfill \\ \hfill \\ \begin{array}{l}\text{Rate of interest per month = 0}\text{.9787\%}\\ \\ \text{Annual Interest Rate = Rate of Interest per month x 12 = 0}\text{.9787\% x 12 = 11}\text{.744\%}\end{array}\hfill \end{array}$.

Conclusion:

Hence the nominal annual interest rate is calculated.

(c)

To determine

Effective annual interest rate.

Answer to Problem 89P

Effective annual interest rate is 12.3972%.

Explanation of Solution

Given information:

Loan amount : $1,000

Duration: 12 Months

Amount of monthly payment is $ 93.12.

Loan amount is $1,000, Amount of monthly payment is $ 93.12 and Duration is12 Months.

Nominal annual interest rate is calculated as periodic interest rate expressed in terms of a year. For instance, a periodic monthly interest rate is expressed in terms of a year by multiplying the same by 12.

Interest rate per month is calculated at 0.9787% per month. Hence the annual interest rate is calculated as Monthly interest rate multiplied by 12.

$\begin{array}{l}\text{Total Amount Repaid = Amount of monthly payment of \$ 93}\text{.12 x Duration of 12 Months}\hfill \\ \begin{array}{l}\\ \text{Total Amount Repaid = \$1,117}\text{.44}\end{array}\hfill \\ \begin{array}{l}\\ \text{Less: Loan Amount = \$1,000}\end{array}\hfill \\ \begin{array}{l}\\ \text{Interest Paid for 1 Year = \$117}\text{.44}\end{array}\hfill \\ \begin{array}{l}\\ \text{Rate of interest per month = Interest Paid for 1 Year / Loan Amount / 12}\end{array}\hfill \\ \hfill \\ \begin{array}{l}\text{Rate of interest per month = 0}\text{.9787\%}\\ \\ \text{Annual Interest Rate = Rate of Interest per month x 12 = 0}\text{.9787\% x 12 = 11}\text{.744\%}\end{array}\hfill \end{array}$

Effective Interest rate is calculated using the following formula:

$\begin{array}{l}{\text{E=(1+i/n)}}^{\text{n}}\text{-1}\\ \\ \text{Where;}\\ \\ \text{i=Annual interest rate}\\ \\ \text{n=Number of periods}\\ \\ \text{Substituting the above values in the equation we get,}\\ \\ \text{E = ( 1+ 0}{\text{.11744/12 )}}^{\text{12}}\text{- 1}\\ \\ \text{E = 12}\text{.3972\%}\end{array}$

Thus, effective interest rate is 12.3972%

Conclusion:

Hence the Effective annual interest rate is calculated.