Question

1a. Of the choice listed below, with all else equal, which choice would be the most beneficial in your section of a savings account that would earn the most interest over time?

(a) An account that is compounded yearly at 5.7% annual interest.

(b) An account that is compounded quarterly at 3.05% annual interest.

(c) An account that is compounded yearly at 3.4% annual interest.

(d) An account that is compounded monthly at 3.5% annual interest.

1b. Second, The Smith family borrowed $300,000 to purchase a home. Calculate their monthly payments for a 30 year loan at 4% annual interest.

(a) $1365.78

(b) $1432.25

(c) $1897.13

(d) $1745.33

1c. Lastly, The amount owed on a loan after 8 months of payments is $151,455. If the annual interest rate is 6%, how much of the next monthly payment of the $878 goes toward paying off the principle (loan amount) during this month?

(a) $29.73

(b) $757.28

(c) $878.00

(d) $120.73

Answer 1

1a)

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

n = number of compounds

a) EAR = 5.7%

b) EAR = (1+0.0305/4)^4 - 1 = 3.085%

c) EAR = 3.4%

d) EAR = (1+0.0305/12)^12 -1 = 3.092%

hence choose a)

1b)

Loan amount = Present value of future monthly payments = monthly payment * [1-(1+i)^-n]/i

i = interest rate per period

n = numbber of periods

monthly payment * [1-(1+0.04/12)^-360]/(0.04/12) = 300000

=>

monthly payment = 1432.25

choose b)

1c)

interest = 151455 * 0.06/12

= 757.275

principal = 878 - 757.28

= 120.73

choose d)