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Homework answers / question archive / You have an outstanding student loan with required payments of $550 per month for the next four years

You have an outstanding student loan with required payments of $550 per month for the next four years

Finance

You have an outstanding student loan with required payments of $550 per month for the next four years. The interest rate on the loan is 10% APR (monthly). You are considering making an extra payment of $150 today (that is, you will pay an extra $150 that you are not required to pay). If you are required to continue to make payments of $550 per month until the loan is paid off, what is the amount of your final payment? What effective rate of return (expressed as an APR with monthly compounding) have you earned on the $150? 
If you are required to continue to make payments of $550 per month until the loan is paid off, what is the amount of your final payment? 
The amount of your final payment is $ 
. (Round to the nearest cent.) 

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First we Calculate the current balance using PV Function in Excel:

=-pv(rate,nper,pmt,fv)

Here,
PV = Current Balance = ?

Rate = 10%/12 

Nper = 4*12 = 48 months

PMT = $550

FV = $0

Substituting the values in formula:

=-pv(10%/12,48,550,0)

PV or Current Balance = $21,685.49

 

Current Balance after Extra Payment = $21,685.49-$150 = $21,535.49

 

Now we calculate Final Payment using FV Function in Excel:

=fv(rate,nper,pmt,-pv)

Here,

FV = Final Payment = ?

Rate = 10%/12

Nper =  4*12 = 48 months

PMT = $550

PV = $21,535.49

Substituting the values in formula:

=fv(10%/12,48,550,-21535.49)

FV or Final Payment = $223.40
 

 

Computation of Effective Rate of Return:

Effective Rate of Return =((223.40/150)^(1/(4*12))-1)*12 

Effective Rate of Return = 10.00%

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