Question

Vinny borrowed $20,000 for 10 years at 5.3 percent compounded monthly. What will the ending balance be after Vinny has made one year of payments?

Group of answer choices

$18,441.59

$18,307.97

$18,574.63

$18,707.09

Answer 1

PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream	$            20,000
PMT = the dollar amount of each annuity payment	To be computed
r = the effective interest rate (also known as the discount rate)	5.43%	((1+5.3%/12)^12)-1)
i= nominal rate of interest	5.30%
n = the number of periods in which payments will be made	10
PV of annuity=	PMT x (((1-(1 + r) ^- n)) / i)
20000=	PMT* (((1-(1 + 5.43%) ^- 10)) /5.30%)
Annual payment=	20000/ (((1-(1 + 5.43%) ^- 10)) /5.30%)
Annual payment=	$         2,580.91
FV of annuity
P = PMT x ((((1 + r) ^ n) - 1) / i)
Where:
P = the future value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	$         2,580.91
r = the effective interest rate (also known as the discount rate)	5.43%	((1+5.3%/12)^12)-1)
i= nominal rate of interest	5.30%
n = the number of periods in which payments will be made	1
Future value of 1 year of payments=	PMT x ((((1 + r) ^ n) - 1) / i)
Future value of 1 year of payments=	2580.91* ((((1 + 5.43%) ^ 1) - 1) / 5.30%)
Future value of 1 year of payments=	$         2,644.54
Loan balance after 1 year	FV of initial loan at T1- FV of 1 year payments
FV of loan at T1=	=20000*(1+5.43%)
FV of loan at T1=	$       21,086.13
Loan balance after 1 year	21086.13-2644.22
Loan balance after 1 year	$       18,441.59