if i have to pay back a loan of 10 million over the next 5 yrs. How much are my yearly payments if each subsequent payment is 15% less than the previous year?
What is the interest rate? Zero?
If there is zero interest rate on the remaining balance, and if the first payment occurs at the end of the first year, then let the first payment be X and you have
X + 0.85 X + (0.85)^2 X + (0.85)^3 X = 10^6.
3.186625 X = 10^6
Solve that for X.
X = $313,811.63
next payment = $266,739.89
etc.
I made two careless errors in my previous answer. The total amount due is 10 million, not one million, and I forgot to ionclude the fifth payment.
The series of five payments ends with the one at the end of the fifth year, (0.85)^4*X
This makes a total payment of 3.70863125X equal to 10 million dollars. The first payment (X) should be X = 2,696,412
To calculate your yearly payments for a loan of $10 million over the next 5 years, with each subsequent payment being 15% less than the previous year, you can use the formula for the sum of a geometric series.
Let the first payment be X.
Then, the second payment will be 0.85X (15% less than the first payment).
The third payment will be (0.85)^2 X (15% less than the second payment).
The fourth payment will be (0.85)^3 X (15% less than the third payment).
And the fifth payment (at the end of the fifth year) will be (0.85)^4 X (15% less than the fourth payment).
The sum of these five payments should equal $10 million.
So, the equation to solve is:
X + 0.85X + (0.85)^2 X + (0.85)^3 X + (0.85)^4 X = $10 million
Simplifying the equation:
1X + 0.85X + (0.85)^2 X + (0.85)^3 X + (0.85)^4 X = $10 million
To calculate X, we can solve for it using the equation:
10 million = X (1 + 0.85 + (0.85)^2 + (0.85)^3 + (0.85)^4)
Rearranging the equation:
X = 10 million / (1 + 0.85 + (0.85)^2 + (0.85)^3 + (0.85)^4)
Calculating the value of X:
X = $2,696,412
So, your first payment should be $2,696,412.
To calculate the subsequent payments, you can multiply the previous payment by 0.85 to get the reduced amount.
The second payment: 0.85 * $2,696,412 = $2,292,950
The third payment: 0.85 * $2,292,950 = $1,948,008
The fourth payment: 0.85 * $1,948,008 = $1,655,807
And the fifth payment: 0.85 * $1,655,807 = $1,407,436
Therefore, your yearly payments for the loan will be as follows:
Year 1: $2,696,412
Year 2: $2,292,950
Year 3: $1,948,008
Year 4: $1,655,807
Year 5: $1,407,436