Question

How much is the equivalent present value in year 0 for a 5-year annuity, starting at the end of year 1 with $10,000 at end of each year, at an annual interest rate at 8% per year, compounded quarterly?

An amortized loan is the arrangement that you pay same amount at the end of each period and you pay off the loan after the last payment. If the beginning amount of a 5-year loan is $10,000, the nominal annual interest rate is 8% per year and payments occur monthly, what is the monthly payment amount in this case?

Answer 1

1)

Answer :$39, 672.46

Explanation

Formula;

Present value of annuity = pmt x {1 - (1+R)^-n/R)

PMT = $10000

N = 5 YEARS

RATE = 8 % COMPOUNDED QUARTERLY

EFFECTIVE RATE = (1+ 8%/4)^4 - 1

= 1.08243216 - 1

= 8.2432% per annum

Present value = 10000 x{1 - (1+8.2432%)^-5/8.2432%

=10000 x 3.967246

= $39672.46 or $39672

2)

Information provided:

Present value= $10,000

Time= 5 years*12 = 60 months

Interest rate= 8%/12 = 0.6667% per month

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

PV= -10,000

N= 60

I/Y= 0.6667

Press the CPT key and PMT to compute the amount of monthly loan payment.

The value obtained is 202.76.

Therefore, the amount of monthly loan payment is $202.76.

In case of any query, kindly comment on the solution.