Question

Yvette is considering taking out a loan with a principal of $16,200 from one of two banks. Bank f charges an interest rate of 5.7%, compounded monthly, and requires that the loan be paid off in eight years. Bank g charges an interest rate of 6.2%, compounded monthly, and requires that the loan be paid off in seven years. How would you recommend that yvette choose her loan?

Answer 1

Yvette should choose Bank f if she wants lower EMI but if she wants lowest lifetime cost she should choose Bank g.

Step-by-step explanation:

Yvette is considering taking out a loan of $16,200.

Bank f charges an interest of 5.7% compounded monthly for 8 years.

Bank g charges an interest of 6.2% compounded monthly for 7 years.

First we calculate the monthly EMI for both banks.

$EMI=\frac{P\times r(1+r)^n}{(1+r)^n-1}$

P = Principal amount ($16,200)

r = monthly interest rate (5.7% annually) 5.7/12 = 0.475/100 = 0.00475

n = number of monthly payments (12×8) = 96

Now put the values :

$=\frac{16,200\times 0.00475(1+0.00475)^{96}}{(1+0.00475)^{96}-1}$

$=\frac{16200\times 0.00475(1.00475)^{96}}{1.00475^{96}-1}$

$=\frac{121.27689}{1.576048-1}$

$=\frac{121.27689}{0.576048}$

= 210.53

Monthly EMI for Bank f = 210.53

Total interest to Bank f = (210.53 × 96) - 16200 = $4010.88

Now we calculate monthly EMI to Bank g.

r = 6.2% (6.2/12) = 0.51666% = 0.005166

n = 12 × 7 = 84 months

$EMI=\frac{16200\times 0.00516(1+0.00516)^{84}}{1+0.00516^{84}-1}$

$=\frac{16200\tmes 0.00516(1.00516)^{84}}{1.00516^{84}-1}$

$=\frac{128.801618}{1.540837-1}$

$=\frac{128.801618}{0.540837}$

= $238.15

Monthly EMI to Bank g = $238.15

Interest to Bank g = (238.15 × 84) - 16200 = $3804.60

Yvette should choose Bank f if she wants lower EMI but if she wants lowest lifetime cost she should choose Bank g.

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