Question

An investor has $60,000 to invest in a $280,000 property. He can obtain either a $220,000 loan at 9.5 percent for 20 years or a $180,000 loan at 9 percent for 20 years and a second mortgage for $40,000 at 13 percent for 20 years. All loans require monthly payments and are fully amortizing.

a1. What is the total monthly payment of the two loans?

$ 2088.14

a2. What is the cost of the combined loan?

_____%

a3. What is the cost of the single loan?

_____%

Answer 1

a2) = 9.76%

Explanation =

PV = 180000, i = 0.75 per month n = 240 (20x12), P/Y = 12,

solving for PMT

PMT = (r ×P)/1-(1+r)^-n

= (0.0075×180000)/1-(1+0.0075)^-240

we get PMT = $1619.51 and

PV = 40000, i = 13, n = 240(20×12) , P/Y = 12 ,

we get PMT = $468.63

To figure out the effective cost, PV = 220000 (180000 + 40000), PMT = $2088.14, n=240, P/Y = 12,

2088.14 = (r × 220000)/1-(1+r)^-240

On solving for r

We get r = 0.8133%

Therefore i = 0.8133×12 = 9.76%

a3) answer = 9.5%

As their is no additional fees the cost of the single loan will be the rate of interest i.e. 9.5%

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