Question

1. What is the value to you today a $50,000 lump-sum that you will receive in 5 years if you could invest your money at 6% compounding monthly? (rate is on annualized bases)

2. You invest $5,000 today with the expectation that this investment will return $100 monthly for the next 5 years. What is your expected annual rate of return?

Answer 1

Answer 1

Future value to be received =50000

interest rate compounded monthly = 6%

rate per month (i) =6%/12 = 0.5%

number of months in 5 years (n) =5*12 = 60

present value = future value/(1+i)^n

=50000/(1+0.5%)^60

=$37,068.61

So value today is $37,068.61

b.

per month amount received (P) =100

number of total months (n) =5*12 = 60

present value = 5000

Present value of annuity formula = P*(1-(1/(1+i)^n))/i

5000=100*(1-(1/(1+i)^60))/i

we will calculate i or monthly rate by trial and error method

Assume i is 0.6%

PV =100*(1-(1/(1+0.6%)^60))/0.6%

=5026.213003

Assume i is 0.65%

PV =100*(1-(1/(1+0.65%)^60))/0.65%

=4955.201803

interpolation formula = lower rate +((uper rate - lower rate)*(Uper price - bond actual price)/(uper price - lower price))

0.6% +((0.65%-0.6%)*(5026.213003-5000)/(5026.213003-4955.201803))

=0.006184569497

Annual rate = monthly rate *number of months in year

=0.006184569497*12

=0.07421483396 or 7.42%

So expected annual rate of return is 7.42%