Question

You borrowed $4,000.00 at 1% per month and agreed to repay in equal monthly payments over the next 3 years. What is your monthly payment? 3. You borrowed $10,000.00 which is to be repaid in equal quarterly payments of $1,336.00 over the next 2 years 4. a) Determine the interest rate per interest period based on quarterly compounding. b) What are the nominal and effective interest rates?

Answer 1

3. Rate of interest per year = (rate per month) $\times$ 12 = 1% $\times$ 12 = 12%

We know, $I = P.i.t$ .......(1) where, I is the total interest, P is the Principal amount, t is the total time.

Using equation (1) We obtain I = $(4000 $\times$ 12% $\times$ 3) = $ 1440

That is the total interest to be paid during the 3 years = Principal amount + Total Interest

= $(4000 +1440) = $5440

Therefore, his monthly payment will be $(5440 $\div$ 36) = $ 151.11

4. a) To calculate the interest rate per interest period based on quarterly compounding, we use the formula $A=P(1+r)^{t}$

  $A=P(1+\frac{r}{n})^{nt}$ Where, A = Accrued Amount (that is Principal + Interest)

P = Principal amount

I = Interest Amount

r = Annual Nominal rate of interest in decimal

t = number of year

n= number of compounding period per year

Since we have to calculate r, then we can write the formula as

$r = n \left [ \left ( A/P \right )^{1/nt} -1\right ]$

$r = 4 \left [ \left ( 11336/10000 \right )^{1/4 \times 2} -1\right ]$  

r = 0.0632

Therefore the compounding interest rate is R = r * 100 = 6.32%

b) The nominal rate is calculated on the basis of annual period. It is the simple interest rate that are calculated without considering the compounding period.

Whereas, effective interest rate is calculated by considering the compounding periods throughout a payment plan.

Nominal Interest rate is less than the effective interest rate.