Question

9 . Implied interest rate and period Consider the case of the following annuities, and the need to compute either their expected rate of return or duration. Jacob needed money for some unexpected expenses, so he borrowed $2,138.41 from a friend and agreed to repay the loan in three equal installments of $800 at the end of each year. The agreement is offering an implied interest rate of . Jacob’s friend, Devan, wants to go to business school. While his father will share some of the expenses, Devan still needs to put in the rest on his own. But Devan has no money saved for it yet. According to his calculations, it will cost him $31,897 to complete the business program, including tuition, cost of living, and other expenses. He has decided to deposit $3,800 at the end of every year in a mutual fund, from which he expects to earn a fixed 6% rate of return. It will take approximately for Devan to save enough money to go to business school.

Answer 1

Answer:

IRR 6% for Jabob

His friend will need 12 years saving cash to obtain their collegue funds.

Explanation:

We will solve for the rate being the annuity of 3 payment of 800

and the present value 2,138.41

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$  

C 800

time 3

PV 2,138.41

rate ?

$800 \times \frac{1-(1+x)^{-3} }{x} = 2,138.41$  

To solve we can use excel, a financial calculator or trial and error

For excel we will do the following:

write the list of cash through the loan life:

-2,138.41

+800

+800

+800

then we write in the empy cell

=IRR(

select the values and press enter

This will give the IRR which is 6%

For the second assignment:

we need to solve for time:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$  

C    3,800

time            n  

rate            0.06

PV $31,897

$3800 \times \frac{1-(1+0.06)^{-n} }{0.06} = 31,897$  

 We work out the formula:

$(1+0.06)^{-n} = \frac{31,897\times 0.06}{3,800}$

Now we solve the right side and apply logarithmic properties

$-n = \frac{log0.503636842 }{log1.06}$

-n = -11.77128325

n = 11.77

It will take 12 years to obtain their target amount