what single payment nine months hence will be equivalent to the two original debts?

Question

~~Donna owes a)$500 due in six month and b)$1,000 plus 8% interest due in three months. If money is worth 6%, what single payment nine months hence will be equivalent to the two original debts?

Answer 1

There is some ambiguity in this question, so this is my interpretation.

I assume that the $500 has a present day value of 500/(1+0.06/2)=$485.44. This is based on the 6% rate applied to money and means that in 6 months’ time, the value of the money will have risen to cancel the debt of $500. If the money is paid late the $500 will gain interest, so at 9 months, the debt will include 3 months’ interest at 6%=$7.50 making the debt at 9 months $507.50.

I assume that no interest will be added to $1000 until the debt is paid 6 months after the 3-month due date. The amount to be paid in 9 months=1000(1+0.08/2)=$1040.

The total payment in 9 months is 507.50+1040=$1547.50.

However, if the worth of the money also has to be taken into consideration on top of the interest then a further 6 months’ interest has to be added for the $1000 debt at 6%=1000×0.06/2=$30, making the payment $1577.50.