A debt of [MATH]€ 10,000[/MATH] contracted 5 years ago had to be repaid with a single payment [MATH]X[/MATH] after 10 years with compound interest of [MATH]10\%[/MATH].
Today the creditor assigns the right to collect the amount in 5 years for [MATH]€ 10,000[/MATH] today and a further sum [MATH]Y [/MATH] in a year.
To calculate:
A) The payment originally envisaged [MATH]X[/MATH]B) The further sum [MATH]Y[/MATH]
Here's how I tried to do the math:
[MATH]C_1=10000 \\ t_1=10 \\ i_1=10\% \\ M=?[/MATH][MATH]C_2 = 10000 \\ t_2=5 \\ i_2=? \\ Y=?[/MATH]
[MATH]M=10000*(1+0.10)^{10} = 25937,4246[/MATH] (1)
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[MATH]25937,4246 = 10000 * (1+i_2)^5 [/MATH] (2)
[MATH]i_2 = \sqrt[5]{\frac{25937,4246}{10000}} - 1= 0.21 = 21\% [/MATH] (3)
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[MATH]25937.4746 = 10000 * (1+0.10)^5 + Y * ( 1+0.10)^1[/MATH] (4_1)
[MATH]16105.10 + 1.1Y = 25937.4246[/MATH] (4_2)
[MATH]Y = \frac{25937.4246 -16105.10}{1.1} = 8938.476909 = 8938.48[/MATH] (4_3)
Are the calculations correct up to this point? I don't know if the interest in (2) is the same of (1) [MATH]= 0.10[/MATH] or i have to calculate it like I did in (3)
And how should I calculate the sum [MATH]Y[/MATH]? Just like I did in (4_1 / 4_3)?
Many thanks in advance!
Today the creditor assigns the right to collect the amount in 5 years for [MATH]€ 10,000[/MATH] today and a further sum [MATH]Y [/MATH] in a year.
To calculate:
A) The payment originally envisaged [MATH]X[/MATH]B) The further sum [MATH]Y[/MATH]
Here's how I tried to do the math:
[MATH]C_1=10000 \\ t_1=10 \\ i_1=10\% \\ M=?[/MATH][MATH]C_2 = 10000 \\ t_2=5 \\ i_2=? \\ Y=?[/MATH]
[MATH]M=10000*(1+0.10)^{10} = 25937,4246[/MATH] (1)
---------------------------------------------------------------------------------------------------------
[MATH]25937,4246 = 10000 * (1+i_2)^5 [/MATH] (2)
[MATH]i_2 = \sqrt[5]{\frac{25937,4246}{10000}} - 1= 0.21 = 21\% [/MATH] (3)
---------------------------------------------------------------------------------------------------------
[MATH]25937.4746 = 10000 * (1+0.10)^5 + Y * ( 1+0.10)^1[/MATH] (4_1)
[MATH]16105.10 + 1.1Y = 25937.4246[/MATH] (4_2)
[MATH]Y = \frac{25937.4246 -16105.10}{1.1} = 8938.476909 = 8938.48[/MATH] (4_3)
Are the calculations correct up to this point? I don't know if the interest in (2) is the same of (1) [MATH]= 0.10[/MATH] or i have to calculate it like I did in (3)
And how should I calculate the sum [MATH]Y[/MATH]? Just like I did in (4_1 / 4_3)?
Many thanks in advance!