# Reducing Balance Interest Calculation

Ok, I know this should be simple and I should know it but I just can’t figure it out, and I can’t find answers in the book either, so I’m hoping someone on here can help. Question is about mortgages, and says some bloke borrows \$200,000 for 30yrs at 6% p.a. compounded monthly. How much is left owing after 4 years. My approach was to calculate the PMT each month using the calculator, because I want to take the principal amount, reduce it by the amount of these payments each month, then add on the amount of interest accrued over the period. However, I’m stumped. How do I caculate interest at 6% p.a (0.5 % monthly compounded for 48 periods), when the balance reduces each month, i.e. as opposed to compounding where it increases each month. As I write this, I’m feeling very dumb, but my brain is fried!!

do this using your calculator and quite simply. 2nd CLR TVM PV=-200000,N=30*48=1440,I/Y=.5 CPT PMT = 1000.76 Now immediately hit 2nd AMORT P1=48 (After 4 years) Down Arrow P2=49 Down Arrow BAL=199957.88

Calculate the PMT: N=30*12=360, I/Y=6/12=0.5, PV=-200,000, FV=0, cpt PMT=1,199.1 To calculate the remaining payments after 4 years (48 months): N=360-48=312, I/Y=6/12=0.5, PMT=1,199.1, FV=0, cpt PV=-182,229.06 Or use the amortization function, with P1=1, P2=48

What’s P1 and P2 stand for? I’m assuming you can use this for premium bonds as well when computing interest expense? Do they have a function for Discount bonds? to compute principal and interest payments

P1 is when the starting payment month, P2 is the ending payment month. For bonds you have a bond worksheet, but you can also use the Amortization worksheet after using the TVM keys to calculate the missing variable.

So when you put in 1 and 48 you’re saying you want the principle amount after payments 1-48? I have to get comfortable with the bond worksheet functions. Thanks

BAL is the remaining balance on the loan after 48 months, PRN is how much of the principal was paid back in the 48 months, INT is how much was paid in interest over the 48 months.

gotcha. So if you wanted to find out how much principal & interest u paid for one period, like lets say the question asks how much principal and interest was paid in yr 3? you could put in p1 24, p2 36?

The values calculated are cumulative, PRN is the principal repayment, cumulative, over the first X months. To find out how much is paid in interest and principal in a specific year (say 3rd year), you need to figure out how much paid in both principal and interest in the first 2 years (P1=1, P2=24), how much paid in principal and interest in the first 3 years (P1=1, P2=36) and deduct one from the other. Your P1 will be the first month of payment, and your payment starts in month 1, not in month 24. You could put P1=24 and P2=36 only after replacement of the PV with the value of the remaining balance at P=24.

Strike the last sentence, when you replace the remaining value, use P1=1, P2=12 to calculate principal repayment and interest payment over 1 year.