last year 92005-2006) you took out a a student loan for $12,000. this year (2006-2007), you got one for $11,000. Next year (2007-2008) you plan on borrowing $10,000. You won't take a long out the following year (2008-2009), and you graduate in 209, if you want to pay the loan back in 10 equal annnual payment and the interest rate is 4%, what will your yearly payments be?
I can't use excel or anything like to solve these problems.
I have to use equations such as F=P(F/p,i,n) or vice versa with P and F.
or A=P(A/P,i,n) etc.
To solve this problem using the provided equations, we need to calculate the present value (P) or future value (F) of the loan, as well as the annual payment (A). Let's break it down step by step:
Step 1: Calculate the present value of each loan using the formula P = F/(1+i)^n, where P is the present value, F is the future value, i is the interest rate, and n is the number of periods.
For the first loan (in 2005-2006):
P1 = $12,000/(1+0.04)^1 = $11,538.46
For the second loan (in 2006-2007):
P2 = $11,000/(1+0.04)^1 = $10,576.92
For the third loan (in 2007-2008):
P3 = $10,000/(1+0.04)^1 = $9,615.38
As you won't take out a loan in 2008-2009, there is no need to calculate the present value for that year.
Step 2: Calculate the total present value of the three loans:
Total Present Value (TPV) = P1 + P2 + P3 = $11,538.46 + $10,576.92 + $9,615.38 = $31,730.76
Step 3: Calculate the annual payment using the formula A = TPV/(A/P,i,n), where A is the annual payment.
To simplify this calculation, we can assume n = 10 (as you want to pay back the loan in 10 equal annual payments).
A = TPV/(A/P,i,10)
A = $31,730.76/(A/P,0.04,10)
Using the A/P formula, we can rewrite this as:
A = $31,730.76/((1 - (1+0.04)^(-10))/0.04)
Simplifying further:
A = $31,730.76/((1 - 0.6755608303)/0.04)
A = $31,730.76/(0.3244391697/0.04)
A = $31,730.76/8.11097924345
A ≈ $3,912.65
Therefore, the yearly payments to pay back the loan in 10 equal annual payments would be approximately $3,912.65.