Question

A couple has just purchased a home for $312,100.00. They will pay 20% down in cash, and finance the remaining balance. The mortgage broker has gotten them a mortgage rate of 5.64% APR with monthly compounding. The mortgage has a term of 30 years.

How much interest is paid on the first payment?

A couple has just purchased a home for $312,100.00. They will pay 20% down in cash, and finance the remaining balance. The mortgage broker has gotten them a mortgage rate of 5.64% APR with monthly compounding. The mortgage has a term of 30 years.

How much interest is paid in the first year?

Answer 1

Answer :

Calculation of Interest paid on First payment :

Interest paid on first payment can be calculated using IPMT function of excel :

=IPMT(rate,per,nper,pv,fv)

where

rate is the rate of interest per period i.e 5.64% / 12 = 0.47% (Divided by 12 as monthly compounding)

per is taken to be 1 as interest needs to be calculated for 1st payment

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

pv is the loan amount i.e 312,100 * 80% = 249680

fv is futire value i.e 0

=IPMT(0.47%,1,360,-249680,0)

On solving

Interest on first payment is 1173.50

Calculation of interest paid in year 1

Interest paid on first payment can be calculated using CUMIPMT function of excel :

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

where

rate is the rate of interest per period i.e 5.64% / 12 = 0.47% (Divided by 12 as monthly compounding)

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

pv is the loan amount i.e 312,100 * 80% = 249680

start period is taken as 1

end period is taken as 12

type 0

=-CUMIPMT(0.47%,360,-249680,1,12,0)

therefore cumulative interest for year 1 is 13998.08