A loan of $13,000 with interest at 10% compounded semi-annually is repaid by payments of $942

Answer 1

Loan amount (PV)= 13000

Quarterly or 3 monthly payment (p)= 942

Rate is 10% comoounded Semiannual.

So Semiannual rate = 10%/2= 5%

Effective Semiannual rate formula = ((1+3 month period rate)^number of 3 month periods in Semiannual year)-1

5% = ((1+I)^2)-1

1+0.05=( 1+I)^2

(1.05)^(1/2)= 1+I

I=1.0246950766-1

I or quarterly rate = 0.0246950766

Loan value or PV of Annuity Formula = P*(1-(1/(1+I)^n))/i

N is to be Calculated by trial and error method

Assume n= 12

PV = 945*(1-(1/(1+0.0246950766)^12))/0.0246950766

=9711.508658

Assume n= 13

PV = 945*(1-(1/(1+0.0246950766)^13))/0.0246950766

=10399.68758

Interpolation Formula = upper n-((upper n- lower n)/(upper Value - lower Value)*(upper Value - Actual Value))

=13-((13-12)/(10399.68758-9711.508658)*(10399.68758-10000))

=12.42 or 13

So Required Payment to amortize Loan is 13 Payment

B.

Payment made in 2 Years =2*4= 8

Number of payment left after 2 Years (n)= 12.42-8

=4.42

Oustanding Balance formula = P*(1-(1/(1+i)^n))/i

= 945*(1-(1/(1+0.0246950766)^4.42))/0.0246950766

=3911.489573

So payout figure will be $3911.49

C.

Total cost of Loan = (Number Of Payment made*Payment Amount)+payout figure - Loan Amount

=(8*945)+3911.489573-10000

=1471.489573

So Cost of Loan is $1471.49