Question

You borrowed some money on a thirty-year mortgage at 3.5%, compounded monthly. Your payments are $950 per month. How much will you pay in interest in the sixth year of this mortgage?

Group of answer choices

$6,565

$7,119

$7,299

$6,933

b)

how much principal does the homeowner pay the first year?

Group of answer choices

$7,340

$4,060

$7,033

$4,835

Answer 1

Answer : Correct Option is 6565

Calculations :

In order to determine the interest we first need to determine the amount borrowed.

Using PV function of Excel :

=PV(rate,nper,pmt,fv)

where rate is the rate of interest i.e 3.5% / 12 (Divided by 12 as monthly compounding)

nper is the number of years to maturity i.e 30 * 12 = 360 (Multiplied by 12 as monthly compounding)

pmt is the per month payment i.e 950

fv is future value i.e 0

=PV(3.5%/12,360,-950,0)

Therefore Amount Borrowed = 211560.24

Now we will calculate the amount of Interest using CUMIPMT

=CUMIPMT(rate,nper,pv,start_period,end_period,type)

where

rate is the rate of interest per period i.e 3.5% / 12

nper is the number of payments i.e 30 * 12 = 360

pv is Present Value calculated above i.e 211560.24

start_period is 61

end_period is 72

type 0

=-CUMIPMT(3.5%/12,360,-211560.24,61,72,0)

Therefore Interest paid in 6th year is 6565

(b.) Correct option is 4060

=CUMPRINC(rate,nper,pv,start_period,end_period,type)

where

where

rate is the rate of interest per period i.e 3.5% / 12

nper is the number of payments i.e 30 * 12 = 360

pv is Present Value calculated above i.e 211560.24

start_period is 1

end_period is 12

type 0

=-CUMPRINC(3.5%/12,360,211560.24,1,12,0)

Therefore Principal paid in 1st years is 4060