Question

Left Bank has a standing rate of 7.9% (APR) for all bank loans and requires monthly payments. What is the monthly payment if a loan is for

​(a​) $140,000 for 5 ​years

(b​) $255,000 for 10 ​years

​(c​) $1,500,000 for 25 ​years

What is the effective annual rate of each of these​ loans?

Answer 1

a.Information provided:

Present value= $140,000

Time= 5 years*12= 60 months

Interest rate= 7.9%/12= 0.6583% per month

The monthly payment is computed by entering the below in a financial calculator:

PV= -140,000

N= 60

I/Y= 0.6583

Press the CPT key and PMT to compute the monthly payment.

The value obtained is 2,831.97.

Therefore, the monthly payment is $2,831.97.

b.Information provided:

Present value= $255,000

Time= 10 years*12= 120 months

Interest rate= 7.9%/12= 0.6583% per month

The monthly payment is computed by entering the below in a financial calculator:

PV= -255,000

N= 120

I/Y= 0.6583

Press the CPT key and PMT to compute the monthly payment.

The value obtained is 3,080.34.

Therefore, the monthly payment is $3,080.34.

c.Information provided:

Present value= $1,500,000

Time= 25 years*12= 300 months

Interest rate= 7.9%/12= 0.6583% per month

The monthly payment is computed by entering the below in a financial calculator:

PV= -1,500,000

N= 300

I/Y= 0.6583

Press the CPT key and PMT to compute the monthly payment.

The value obtained is 11,477.66

Therefore, the monthly payment is $11,477.66

Effective annual rate is calculated using the below formula:

EAR= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

EAR= (1+0.079/12)^12-1

        = 1.0819-1

        = 0.0819*100= 8.19%

Therefore, the effective annual rate is 8.19%.

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