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Need some help on this calculation:

Loan Amount: $377100

Down payment: $41900

Monthly payment: $5998

Balloon payment at the end: $206540

Tenor: 36 months

I want to know how to calculate the effective interest rate. Can anyone give me an answer? I am using Casio F100 Financial Calculator, please teach me how to use this calculator to calculate this.

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  • Appreciate for all reply. So the conclusion is by our manual calculation, the effective interest rate is 11.063%, also the same as automated webpage calculator, right?
    – north
    Mar 26 '19 at 2:37
  • No, the effective rate is 5.22% as shown in the webpage calculator screenshot below.
    – Chris Degnen
    Mar 26 '19 at 14:57
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For time value of money calculator computation:

PV = 377100

FV = 206540

N = 36

PMT = 5998 (note, your brand of calculator might want payment to be a negative number)

Calculate r

This gives you back the rate each month. Multiply by 12 for annual rate or (1+r)^12 for APR

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from this web site https://www.mortgagecalculator.org/calcs/balloon.php, it shows the effective interest rate is 11.02% (amount borrowed: 377100, long term in years: 3, Upfront payment: 41900, loan fees: 0, balloon payment at end: 206540, monthly payment: 5988.99) How come the interest rate is much high that we calculated? Please help.

Editing the OP's post

With r = 0.00425237 per month, as calculated in the addendum.

Nominal annual interest rate, compounded monthly 12 r = 5.102844 %

The results below are based on 36 payments of 5998 plus a final payment of 206540 at the end of month 36. The total paid in month 36 is 212538.

enter image description here

Top and bottom of amortisation table. Note the principal amount: 377100.

enter image description here

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  • Thx Chris, but for "Amount Borrowed", should be 419000 or 377100? Since the house is 419000, and I need to pay 10% down payment, so the Amount borrowed, should be 377100, right? – north 27 secs ago
    – north
    Mar 26 '19 at 10:02
  • For the website calculator Amount Borrowed should be 419000 and Upfront Payment should be 41900. The calculator automatically deducts the upfront payment from the amount borrowed to obtain the Principal: 377100, as shown in the Amortization Schedule. Try setting the website calculator up as I have shown and check the amortization schedule.
    – Chris Degnen
    Mar 26 '19 at 10:25
  • Thx Chris! Much appreciate for your help! Now, is much clear. Thanks a lot!
    – north
    Mar 26 '19 at 15:15
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The value of the loan is equal to the sum of the discounted values of the repayments.

enter image description here

∴ b = ((1 + r) (m + (1 + r)^n (r s - m)))/r

and m = (r ((1 + r)^(1 + n) s - b))/((1 + r) ((1 + r)^n - 1))

where

s = present value of loan
m = periodic repayment
r = periodic rate
b = balloon payment
n = number of periods (or payments) before the balloon

There is no formula for the periodic rate r. You will need to solve for it using one of the above equations.

s = 377100
m = 5998
b = 206540
n = 35

Solving s = (m - m (1 + r)^-n)/r + b/(1 + r)^(n + 1) for r

∴ r = 0.00372937

So the effective annual rate is (1 + r)^12 - 1 = 4.56819 %

This assumes full amortisation, i.e. 35 payments of 5998 and a final one of 206540 at the end of month 36.

"With full amortization, the amortization schedule has been set so that the last periodical payment comprises the final portion of principal still due."

Addendum

With 36 payments of 5998 and a payment of 206540 at the end of month 36

s = 377100
m = 5998
b = 206540 + m = 212538
n = 35

∴ r = 0.00425237

The effective annual rate is (1 + r)^12 - 1 = 5.2239 %

Confiming with Excel

enter image description here

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  • Thx again for the reply, Mr. Chris. So the previous ans ~10% is incorrect? Now is only 4.56819%? Can I say that effective annual rate is APR? Also, my repayment schedule is 36 payments of 5998, then last balloon payment is 206540.
    – north
    Mar 25 '19 at 11:02
  • And just to be clear, the 206540 is paid in month 36 along with the 36th payment of 5998?
    – Chris Degnen
    Mar 25 '19 at 11:24
  • after 36 mth of 5998, then one more final payment is 206540
    – north
    Mar 25 '19 at 14:59
  • With 36 payments of 5998 and a payment of 206540 at the end of month 36 Also deducting the downpayment from the principal<---377100 is already deducted the down pament from 419000 (ie 41900), so s = 377100
    – north
    Mar 26 '19 at 6:32
  • Then your effective rate is 5.2239% as shown in the addendum above.
    – Chris Degnen
    Mar 26 '19 at 7:17

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