Question

1. Ben decided to purchase a $200,000 house. The interest rate is at 4.5%, paid monthly, and is a thirty-year loan. He plans to borrow the entire $200,000 for the purchase. How much principal and interest will Ben pay over the first 10 years of the loan?

N=

I= 4.5%

PV= 200,000

PMT=

FV=

Cumulative principal payments over 5 years=

Cumulative interest charges over 5 years=

Answer 1

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          200,000
Rate of interest per period:
Annual rate of interest		4.500%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.045 /12 =	0.3750%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	30.00
Total number of payments	N	30 × 12 =	360
Period payment using the formula	=	[ 200000 × 0.00375 × (1+0.00375)^360] / [(1+0.00375 ^360 -1]
Monthly payment	=	$                                                         1,013.37

In five years:

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	200,000.00
Rate of interest	r=	0.3750%
nth payment	n=	60
Payment	P=	1,013.37
Loan balance	=	200000*(1+0.00375)^60 - 1013.37*[(1+0.00375)^60-1]/0.00375
Loan balance	=	182,315.83

Loan amount		$                                                                     200,000.00
Less: current balance		$                                                                     182,315.83
Principal paid		$                                                                       17,684.17
Total payments:
Monthly payment × 12 =		$                                                                       60,802.24
Less: principal paid		$                                                                       17,684.17
Interest paid		$                                                                       43,118.07

Cumulative principal payments over 5 years= 17,684.17

Cumulative interest charges over 5 years= 43,118.07