Question

A family takes out a mortgage for $250,000 from the local bank. The loan is for 30 years of monthly payments at a 6% APR (monthly compounding).   What will the family’s balance be on the mortgage after 5 years?                      

a. 209,214.31

b. 212,469.24

c. 232,635.89

d. 234,294.86

e. 209,214.31

Answer 1

Sol:

Loan amount (PV) = $250,000

Rate (r) = 6% (Monthly) = 6/12 = 0.50%

Period (NPER) = 30 years (Monthly) = 30 x 12 = 360 periods

To determine balance be on the mortgage after 5 years:

PV	250000
NPER	360
Rate	0.50%
PMT (Monthly Payment)	-$1498.88
NPER	60
PMT	-1498.88
Rate	0.50%
Future value (FV) of loan paid	104576.65
FV after 5 years	337212.54
Outstanding balance remaining	$232,635.89

Therefore balance be on the mortgage after 5 years will be $232,635.89

Answer is c. 232,635.89

Working

A B 250000 1 PV 2 NPER 3 Rate 360 =6%/12 =PMT(B3,B2,B1,0) 4 PMT 5 6 NPER =5*12 7 PMT =B4 8 Rate =B3 9 FV of loan paid =FV(B8,B6,B7,0) 10 FV after 5 years |=B1*(1+B8) “B6 11 Outstanding balance remaining =B10-B9