Question

1. An investor has $60,000 to invest in a $280,000 property. He can obtain either (option A) a $220,000 loan at 9.5 percent for 20 years; or (option B) a $180,000 loan at 8.75 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. How much more would be the effective cost % if you went forward with option A instead of option B. I.e., what is “cost% for A - cost% for B”? (Notes: if the cost is less for option A, don’t forget the negative sign. Input answer without “%” sign, e.g., 5.75% as 5.75.)

2. Refer to the same question. How much more would be the effective cost % if you went forward with option A instead of option B if the second mortgage in option B had a 10-year term instead? (Notes: if the cost is less for option A, don’t forget the negative sign. Input answer without “%” sign, e.g., 5.75% as 5.75.)

Answer 1

1. An investor has $60,000 to invest in a $280,000 property.
(Option A) a $220,000 loan at 9.5 percent for 20 years; or
(Option B) a $180,000 loan at 8.75 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.
How much more would be the effective cost % if you went forward with option A instead of option B. I.e., what is “cost% for A - cost% for B”?
Calculation of Effective Cost =
EMI = [P x R x (1+R)^N]/[(1+R)^N-1],
where,
P stands for the loan amount or principal,
R is the interest rate per month, and
N is the number of monthly instalments.

Option A = [ $220000 * 0.792% * ( 1 + 0.792%)240] / [ ( 1 + 0.792%)240-1]
= [ $1742.40 * 6.6413] / [6.6413-1]
= $11571.80 / 5.6413
= $2051.26 or $2,051 (in round off)
Effective Cost % of Loan = Total Interest / loan Amount* no of yrs.
= [($2051*240 - $220000)] / [($220000) (20 yrs)]
= $272,240 / $220,000 * 20 Yrs
= 6.19% (Assuming Other Cost are Null)

Option B (1st mortgage)
  = [ $180000 * 0.729% * ( 1 + 0.729%)240] / [ ( 1 + 0.729%)240-1]
= [ $1312.20 * 5.7159] / [5.7159-1]
= $7500.40 / 4.7159
= $1590.45 or $1,590 (in round off)
Option B (2nd mortgage)
  = [ $40,000 * 1.083% * ( 1 + 1.083%)240] / [ ( 1 + 1.083%)240-1]
= [ $433.20 * 13.2663] / [13.2663-1]
= $5746.96 / 12.2663
= $468.52 or $469.00 (in round off)

Effective Cost % of Loan = [Interest paid 1st loan / loan Amt* no of yrs.] + [Interest paid 2nd loan / loan Amt* no of yrs.]
= [($1590*240)-$180000 / ($180000 * 20 Yrs)] + [($469*240)-$40000 / ($40000 * 20 Yrs)]
= 5.60% + 9.07%
= 14.67% (Assuming Other Cost are Null)

if we went with Option A then, “Cost% for A - Cost% for B” = 6.19% - 14.67% = -8.48 (Ignoring % sign)

2. if the Second Mortgage in Option B had a 10-year term instead...
Option B (2nd mortgage)
  = [ $40,000 * 1.083% * ( 1 + 1.083%)120] / [ ( 1 + 1.083%)120-1]
= [ $433.20 * 3.6423] / [3.6423-1]
= $1577.84 / 2.6423
= $597.15 or $597.00 (in round off)

Effective Cost % of Loan = [Interest paid 1st loan / loan Amt* no of yrs.] + [Interest paid 2nd loan / loan Amt* no of yrs.]
= [($1590*240)-$180000 / ($180000 * 20 Yrs)] + [($597*120)-$40000 / ($40000 * 10 Yrs)]
= 5.60% + 7.91%
= 13.51% (Assuming Other Cost are Null)

if we went with Option A then, “Cost% for A - Cost% for B” = 6.19% - 13.51% = -7.32 (Ignoring % sign)..