Question

Q1

Return to a What effective interest rate per month, compounded continuously, is equivalent to a nominal rate of 10% per year? 

The effective interest rate per month is _______ %

Q2

Environmental recovery company RexChem Partners plans to finance a site reclamation project that will require a 4-year cleanup period. If the company borrows $4.1 million now, how much will the company have to get at the end of each quarter in order to earn 15% per year, compounded weekly on its investment? Calculate the answer using both formula and spreadsheet function? 

In order to earn 15% per year compounded weekly on its investment at the end of each quarter, the company will have to get $ _______ .

Answer 1

1. Effective Annual Rate = 10%
Effective rate continuously compounded = e^ln(1+r) - 1
ln(1.1) = 0.09531018
Montly rate = 0.09531018/12 = 0.07942515
e^0.07942515 -1 = 0.00797414
Hence, monthly continuous rate = 0.797414%

2. Effective Quarterly rate = (1+(Rate per year/52))^{Number of weeks} =(1+Rate per quarter)⁴,
(1+(0.15/52))²⁰⁸=(1+r)⁴,
r = 16.1583394% per quarter

Now, using the PMT function in excel,
=PMT(16.1583394%,16,-4100000)

7,28,839.57883

per quarter.