Question

You decide to get an ARM loan for $200,000 for 30 years starting at 5.00% with the interest rate adjustment of 2% annual cap and 9% lifetime ceiling. Let's say, based on the inflationary economy, your loan interest rate is projected to increase 2% annually for the next 5 years. What would be your projected monthly payment for the 4th year of your loan?

a. $1,344.26

b. $1,558.32

c. $1,632.59

d. $1,646.25

Answer 1

beginning of T=1

Loan amount = 200,000

Interest rate = 5%

Interest rate per month = 5%/12 = 0.4167%

Time to maturity = 30 years = 12 x 30 = 360 months

Principal repaid till the end of year calculated using CUMPRINC formula in excel = CUMPRINC(rate, nper, PV, start_period, end_period, type) = CUMPRINC(0.4167%,360,200000,1,12) = (2,950.73)

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beginning of T=2

Loan amount = 200,000 - principal repaid in year 1 = 200,000 - 2,950.73 =  197,049.27

Interest rate = 5% + 2% = 7%

Interest rate per month = 7%/12 = 0.5833%

Time to maturity = 30-1 = 29 years = 12 x 29 = 348 months

Principal repaid till the end of year calculated using CUMPRINC formula in excel = CUMPRINC(rate, nper, PV, start_period, end_period, type) = CUMPRINC(0.5833%,348,197,049.27,1,12) =  (2,168.37)

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beginning of T=3

Loan amount = 197,049.27 - 2,168.37 =  194,880.90

Interest rate = 7% + 2% = 9%

Interest rate per month = 9%/12 = 0.75%

Time to maturity = 29-1 = 28 years = 12 x 28 = 336 months

Principal repaid till the end of year calculated using CUMPRINC formula in excel = CUMPRINC(rate, nper, PV, start_period, end_period, type) = CUMPRINC(0.75%,336, 194,880.90,1,12) =  (1,616.05)

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beginning of T=4

Loan amount = 194,880.90 - 1,616.05 =  193,264.85

Interest rate = 9% + 2% = 11%

Interest rate per month = 11%/12 = 0.9167%

Time to maturity = 28 -1 = 27 years = 12 x 27 = 324 months

Monthly payment in the 4th year using PMT function of excel = PMT(Rate, nper, PV) = PMT(0.9167%,324,-193,264.85) = $1,868.77

Hence the correct answer is $1,868.77

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