Question

A debt of $42000 is repaid by making payments of $4500. If interest is 9% compounded monthly, for how long will payments have to be made at the end of every six months? b) What payment made at the end of each year for 18 years will amount to $48000 at 4.2% compounded monthly?

Answer 1

First part:

Appropriate discount rate is:

Particulars	Amount
Given APR	9.00%
Given compounding frequency per year	12
Effective annual rate	9.4%
(1+ 0.09/12)^12 -1
Required compounding frequency per year	2
Req period effective rate	4.5852%
(1+ 0.0938069)^1/2 -1
Required APR	9.17045%
0.04585224*2

n	Number of payments required =	Log [ 1/ [1 - PV× r/ P] ]/ Log(1+r)
PV =	Loan amount	$                         42,000.00
P=	Periodic payment	4,500.00
r=	Rate of interest per period
	Annual interest	9.170450%
	Number of payments per year	2
	Interest rate per period	0.0917045/2=
	Interest rate per period	4.585225%
	Number of payments =	Log [ 1/ (1- 42000 × 0.04585/4500) ]/ Log( 1+ 0.04585)
n=	Number of payments =	12.46
	Years	6.23

It takes 6.23 years for paying loan back.

Second part:

Annual rate of interest is:

Particulars	Amount
Given APR	4.20%
Given compounding frequency per year	12
Effective annual rate	4.281801%
(1+ 0.042/12)^12 -1

Payment required	=	FV*r /[(1+r)^n -1]
Future value	FV	48,000.00
Rate per period	r
Annual interest		4.28180%
Number of payments per year		1
Interest rate per period		0.0428180071986148/1=
Interest rate per period		4.281801%
Number of periods	n
Number of years		18
Periods per year		1
number of periods		18
Period payment	=	48000*0.042818/ [(1+0.042818)^18 -1]
	=	1,823.77

Answer is:

1,823.77

please rate.