Question

A owes $3000 now and $2000 in 4 months. After re-arrangement of payments, he
agreed to pay $X in 6 months and $2X in 8 months from now. Determine the value
of $X with j12 = 12% per annum.

Answer 1

Ans please
owes $3000 now and $2000 in 4 months. After re-arrangement of payments, he
agreed to pay $X in 6 months and $2X in 8 months from now. Determine the value
of $X with j12 = 12% per annum.

Answer 2

$1759.63



Assuming that the interest rate is 12% per annum, the value of $X can be determined using the formula for present value of an annuity:

PV = A * ((1 - (1 / (1 + i)^n)) / i)

where PV is the present value, A is the annuity payment, i is the interest rate, and n is the number of payments.

In this case, the annuity payment is $X, the interest rate is 12% per annum, and the number of payments is 2. Plugging these values into the formula, we get:

PV = X * ((1 - (1 / (1 + 0.12)^2)) / 0.12)

PV = X * ((1 - (1 / 1.2496)) / 0.12)

PV = X * (0.1992 / 0.12)

PV = X * 1.66

Therefore, X = PV / 1.66, and PV = $3000.

X = $3000 / 1.66

X = $1759.63

Paying $3000 now and $2000 in 4 months, the interest rate is $12\%$ p.a.. In this case $j=12\%$ p.a. and $n=4$.
Now you owe $3000$ now and $2000$ in $6$ months time.
So, $X(1+\frac jn)^n=3000$
$X(1+\frac j{12})^{12}=3000$
$X(1+j)^n=3000$
$X(1+j)^4=3000$
$X(1.12)^4=3000$
$X(\frac{1.12^{12}}{1.12^4})=3000$
$X=3000(\frac{1.12^{12}}{1.12^4})$
$X=\frac{3000}{1.12^8}$
$X=\frac{3000}{1.2^8}$
$X\approx 1719.02$
0.12)^6 = $1759.63