Question

(S marks) Seven months ago Amir agreed to pay Robert three payments of ssoo, $700 and $900 in four, twelve and eighteen months from the date of the agreement. No payments have been made and Amir and Robert have renegotiated the terms of the agreement to make one single payment six months from today. If the agreed upon rate of interest was 6% per annum. what is the size of that single payment?

Answer 1

1)

The solution is provided in the image attached below:

I have first calculated the time difference between the due dates of individual payments and the new payment date which is 6 months from now

then I converted the the time difference which was calculated in months to years by dividing the above figures by 12 since the interest rate is per annum

then I calculated the future value of these individual payments 6 months from today,

size of single payment = future value /((1+r)^(6/12))

where r = 6% and 6/12 = no. of years for 6 months

2 payment 3 payment period 7 months ago 4 12 18 time difference between single payment and individual 4 payments (no. of months) 5 Time difference(years) 6 date of agreement (months) 7 single payment due in (months) 8 rate of interest 0.75 0.083333-0.41667 0.06 10 future value of single payment 11 size of single payment 12 2104.15 2043.74

2 payment 3 payment period 7 months ago 500 700 900 4 12 18 time difference between single payment and individual payments 4 (no. of months) 5 Time difference(years) 6 date of agreement (months) 7 single payment due in (months) 8 rate of interest (B6-B3)+B7 B4/12 C4/12 D4/12 0.06 10 future value of single payment 11 size of single payment 12 13 s(B2*((1+88)ng5))+(C2*((1+88)^C5))+(D2*((1+88)^D5)) B10/((1+88(B7/12))