You had an agreement to pay $4,075 in 2 years from now and $6,725 in 5 years from now. What single payment would pay off this debt in one year from now if money earns 7.1% compounded quar

Question

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Answer 1

We can work out the growth rates for 1, 2 and 5 years at 7.1% per annum compounded quarterly.

The quarterly rate is 7.1/4=1.775%.

Growth rates:

1 yr: 1.01775⁴=1.0729 approx

2 yr: 1.01775⁸=1.1511 approx

5 yr: 1.01775²⁰=1.4217 approx

We can apply the growth rates to any of the amounts.

To pay off $4075 in 2 years’ time would have needed an investment of 4075/1.1511=$3539.96 now. In a year’s time this would grow to 3539.96(1.0729)=$3798.07.

To pay off $6725 in 5 years’ time would have needed an investment of 6725/1.4217=$4730.10 now. In a year’s time this would grow to 4730.10(1.0729)=$5074.98.

Therefore the total amount to be paid in a year’s time is 3798.07+5074.98=$8873.05.

This calculation takes into account the fact that the debts are paid early so the amounts to be paid are correspondingly reduced from $10800.

The graph illustrates the calculation.