Question

6. A payment stream consists of three payments: $1000 today, $1500 in 70 days and $2000 in 210 days. What single payment, 60 days from now, is economically equivalent to the payment stream if money can be invested at a rate of 8.5%? 7. If the interest paid on a loan was $350 at an interest rate of 0.3% per month for 5 months, how much was the amount originally borrowed? 12

Answer 1

a. Consider the timeline of the transactions.

One transaction of $1000 today, next in 70 days of $1500 and last in 210 days of $2000. To get the payment after 60 days equivalent of them, we will find the future value of the first payment and the present value of the other two.

Future value of first payment after 60 days

Future value = Present value * (1 + Interest/no. of periods)^(Time)

= 1000*(1+(8.5/365)%)^(60)

= 1014.069

Present value of second payment will be present value in 60 days from now or present value before 10 days

Present value = Future value/(1+ Interest/no. of periods)^time

= 1500/(1+(8.5/365)%)^(10)

= 1496.511

Present value of second payment will be for 210 - 60 = 150 days

= 2000/(1+(8.5/365)%)^(150)

= 1931.351

Total value = 1014.069 + 1496.511 + 1931.351 = 4441.931

b. Let' solve for the future value of $1 after 5 month at 0.3% interest per month

= 1*(1+(0.3)%)^(5)

= 1.01509

$1 gave use $1.01509 after 5 months

Interest is $0.1509 which is 1.509% of $1

So $350 is 1.509% of x * $1

To solve for x

1.509% of x = $350

x = 350/1.509%

= $23,194.16