Question

A loan of €50,000 is being repaid with monthly level payments at the end of each year for 6 years at 5% effective rate. Just after making the payment of the second annuity, it is decided to change the amortization method, the loan is being repaid with constant annual principal repayments for the remaining 3 years at an interest rate of 4.5%.

A) find the outstanding debt just after the payment of the third annuity

Answer 1

Balance after two payments is:

Yearly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                            50,000
Rate of interest per period:
Annual rate of interest		5.000%
Frequency of payment	=	Once in 12 month period
Numer of payments in a year	=	12/12 =	1
Rate of interest per period	R	0.05 /1 =	5.0000%
Total number of payments:
Frequency of payment	=	Once in 12 month period
Number of years of loan repayment	=	6
Total number of payments	N	6 × 1 =	6
Period payment using the formula	=	[ 50000 × 0.05 × (1+0.05)^6] / [(1+0.05 ^6 -1]
Yearly payment	=	$                                                         9,850.87

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	50,000.00
Rate of interest	r=	5.0000%
nth payment	n=	2
Payment	P=	9,850.87
Loan balance	=	50000*(1+0.05)^2 - 9850.87*[(1+0.05)^2-1]/0.05
Loan balance	=	34,930.72

Principal payment in year 3 = 34,930.72/3 = 11,643.57

Outstanding debt after payment of 3rd annuity = 34,930.72 - 11,643.57 = 23,287.15

please rate.