MATH SOLVE

2 months ago

Q:
# 1. Tristan Sandino is selling his motorcycle. His friend, Rudy, is offering to pay cash in the amount of $8,800. Another friend, Costa, has offered payments of $200 monthly for 4 years. What is the present value of Costa's payments? Assume money is worth 3.4%, compounded monthly. a.) $8,963.96 b.) $9,163.96 c.) $9,600.00 2. You are thinking about investing $25,000 in a business with expected returns as follows: costs of $1,250 per quarter for one year, gains of $2,000 per quarter for the next 2 years, and gains of $3,000 per quarter for the next 3 years. What would be your rate of return after 6 years? a.) 15.55% b.) 3.89% c.) 26.36%

Accepted Solution

A:

1. The amortization formula can tell you the present value if the string of payments is made at the end of the month.

A = P(i/n)/(1 -(1 +i/n)^(-nt))

where A is the payment (200), P is the present value, n is the number of compoundings per year (12), and t is the number of years (4).

200 = P(.034/12)/(1 -(1 +.034/12)^-48)

200 = P*0.0223115558

P = 200/0.0223115558 ≈ 8,963.96

This matches the selection ...

a) $8963.96

[Please note that an actual sale would probably require the first payment be made immediately, hence the present value would actually be $8,989.36.]

2. A financial calculator (HP-12c) computes the IRR at 3.889% (per quarter). Hence the annual rate of return is about

4*3.889% ≈ 15.55%

This matches selection ...

a.) 15.55%

A = P(i/n)/(1 -(1 +i/n)^(-nt))

where A is the payment (200), P is the present value, n is the number of compoundings per year (12), and t is the number of years (4).

200 = P(.034/12)/(1 -(1 +.034/12)^-48)

200 = P*0.0223115558

P = 200/0.0223115558 ≈ 8,963.96

This matches the selection ...

a) $8963.96

[Please note that an actual sale would probably require the first payment be made immediately, hence the present value would actually be $8,989.36.]

2. A financial calculator (HP-12c) computes the IRR at 3.889% (per quarter). Hence the annual rate of return is about

4*3.889% ≈ 15.55%

This matches selection ...

a.) 15.55%