1) We receive $3,000 per semester and $87,000 in 9 years from the present. What

Question

1) We receive $3,000 per semester and $87,000 in 9 years from the present.

What ROR did we attain, if we now invest $4,000?

(so I think this means we reveive 3,000 twice a year for 9 years with a lump sum of 87,000 in the 9th year. but I am not sure how to calculate rate of return and what to do with the 4,000 invested amount) Please show formulas and steps

2) We buy an asset for $20,000. We receive money to the tune of ___ per month.

At the end, 4 years later, we are paid $12,000. The ROR is 10%. What was that money receipt?

Explanation / Answer

Answer:-

1.) Investment = $4000

Receive = $3000 per semester

= 3000 * 2 = 6000 per annuam

Toatal receive = 87000

Receive at the end of 9th year = 87000 - (6000*9)

= 87000 - 54000

= 33000

year = 9 year semi-annually (semester)

= 9 * 2 = 18 year [annually]

=(33000*.00003)

=.99

ROR (r) = 70% + [(4289 - 4000) / (4289 - 3751)] * (80% - 70%)

= 70 + [(289) / (538)] * 10

= 70 + (.537) * 10

= 70 + 5.37

= 75.37% [annually]

= 75.37 / 2

= 37.685% [semi-annually]

2.) Investment = $20000

year = 4 years

ROR = 10%

Amount paid at the end of 4th year = 12000

Let Money receipt = x

Investment = Money receipt * PVIFA at (r,n) - Amount paid * PVIF at (r,n)

20000 = x * PVIFA at (10%,4year) - 12000 * PVIF at (10%,4year)

20000 = (x * 3.169) - (12000 * .683)

20000 = 3.169x - 8196

20000 - 8196 = 3.169x

11804 = 3.169x

x = 11804 / 3.169

Money receipt = 3725 (per annuam)

= 3725 / 12

= 310.4 (per month)   

Year Cash Infow PVIF at 70% (Assumed) Present Valve PVIF at 80% (Assumed) Present Valve 1 to 18 3000 1.4285 =(3000*1.4285) =4285.5 1,25 =(3000*1.25) =1.25 18 33000 .0001 =(33000*.0001) =3.3 .00003

=(33000*.00003)

=.99

TOTAL 4289 3751

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