Question

Today, you borrowed $20,000 at 5.5% with quarterly compounding. You have agreed to pay off the loan over 5 years by making equal weekly payments. If you were solving for your unknown weekly payment amount using the annuity present value equation, what interest rate would you use? (Hint: You don't actually need to solve for your unknown payment amount.)

Answer 1

Part A

Effective rate of interest (r) = [(1+i/m)^m] - 1

where

nominal annual rate of interest = 5.5 % or 0.055

nominal interest rate per quarter i = 5.5 % / 4 = 1.375 % per quarter

m - no. of periods compounding per quarter = 13 weeks per quarter

r = ([1+0.01375/13)^13]-1

= (1.001058)^13 - 1

= 1.01384 - 1

= 0.01384 or 1.384 %

Effective rate of interest (r) = 1.384 % per quarter

Part B

Particulars	Amount
Loan Amount	$             20,000.00
Int rate per week	0.10646%
No. of weeks	260

weekly equal Instalemnt = Loan Amount / PVAF (r%, n)
Where r is Int rate per week = 1.384 % / 13 = 0.10646 or 0.0010646

n is No. of weeks = 260
= $ 20000 / PVAF (0.0011 , 260)
= $ 20000 / 227.0141
= $ 88.1

PVAF = [ 1 - [(1+r)^-n]] /r
= [ 1 - [(1+0.00106)^-260]] /0.00106
= [ 1 - [(1.00106)^-260]] /0.00106
= [ 1 - [0.75832]] /0.00106
= [0.24168]] /0.00106
= 227.01



Unknown weekly payment = $ 88.1

please comment if any further assistance is required.