Question

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

Lets say the company receives amount X per quarter

therefore to earn rate of return of 15% we need

X/(1+(15%/52))^13+X/(1+(15%/52))^26+X/(1+(15%/52))^39+X/(1+(15%/52))^52+X/(1+(15%/52))^65+X/(1+(15%/52))^78+X/(1+(15%/52))^91+X/(1+(15%/52))^104+X/(1+(15%/52))^117+X/(1+(15%/52))^130+X/(1+(15%/52))^143+X/(1+(15%/52))^156+X/(1+(15%/52))^169+X/(1+(15%/52))^182+X/(1+(15%/52))^195+X/(1+(15%/52))^208

I have used interest rate to discount equals to (1+(15%/52))^13

Because 1 quarter equals to 13 weeks

X((1/(1+(15%/52))^13)+(1/(1+(15%/52))^26)+(1/(1+(15%/52))^39)+(1/(1+(15%/52))^52)+(1/(1+(15%/52))^65)+(1/(1+(15%/52))^78)+(1/(1+(15%/52))^91)+(1/(1+(15%/52))^104)+(1/(1+(15%/52))^117)+(1/(1+(15%/52))^130)+(1/(1+(15%/52))^143)+(1/(1+(15%/52))^156)+(1/(1+(15%/52))^169)+(1/(1+(15%/52))^182)+(1/(1+(15%/52))^195)+(1/(1+(15%/52))^208)

=15.0838915X

4100000=15.0838915X

X=4100000/15.0839=$271,813.45

hence we need per quarter $271,813.45

Now with the help of excel we use PMT function to evaluate each quarter payment

PMT(rate,nper,PV,0)=PMT(15%/52,16,4100000,0) we get answer as $262,578.3

( This difference is answer is due to ignored higher decimal values in manual calculations by hand)