You owe your parents $19,000 (in present day dollars) and want to repay them in equal amounts the first to occur in 3 years from today and the other in 6 years from today

In the given case, calculation will be made as under:

Here, we will assume that payment to be made after 3rd year and 6th year as x and We will here calculate Present value Factor of 3rd year and 6th year and equate it with Present amount of $ 19000.

Annual interest rate is 7.90% and therefore monthly interest rate is 7.90/12= 0.6583 (monthly compounding)

Present Value of Loan = (Installment at the end of 3rd year * (1+r/1200)^(n*12)) + (Installment at the end of 6th year * (1+r/1200)^(n*12))

here r = Annual rate of interest and therefore it is divided by 12 as said above.

here n = number of years and they are also divided by 12 due to monthly comounding

19000 = (x * (1+0.006583)^36) + (x * (1+0.006583)^72)

19000= (x* (1.006583)^36) + (x* (1.006583)^72)

19000 = (x * 0.789614) + (x * 0.62349)

19000 = 0.78961x + 0.62349 x

19000= 1.4131x

x = 13445.62 approx.

Therefore answer is option (a).

1)

First, we find the spot rates for all maturities

Let the spot rate for 1 year be s1, for 2 year be s2 and so on, then

985 = 1000/((1+s1)^1)

s1 = 1.52284264%

950 = 1000/((1+s2)^2)

s2 = 2.597835209%

910 = 1000/((1+s3)^3)

s3 = 3.19362513%

870 = 1000/((1+s4)^4)

s4 = 3.542867202%

(1)

One year interest rate in one year be k, then

(1+0.0152284264)*(1+k) = (1+0.02597835209)^2

k = 3.684%

(2)

One year interest rate in two years be k, then

(1+k)*(1+0.02597835209)^2 = (1+0.0319362513)^3

k = 4.396%

(3)

One year interest rate in three years be k, then

(1+k)*(1+0.0319362513)^3 = (1+0.03542867202)^4

k = 4.598%