<h3>
Answer: $44,097.56</h3>
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Work Shown:
L = loan amount
8456.40 = amount paid in interest
L+8456.40 = total amount paid back
15 years = 15*12 = 180 months
(L+8456.40)/180 = monthly payment
Well come back to this later, so let A = (L+8456.40)/180
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Given the following
- L = loan amount
- r = 0.024 = annual interest rate in decimal form. This leads to i = r/12 = 0.024/12 = 0.002, which is the monthly interest rate in decimal form.
- n = 180 months
We can form an expression to get us the monthly payment P.
We'll use this monthly payment formula.
P = (L*i)/( 1-(1+i)^(-n) )
So,
P = (L*i)/( 1-(1+i)^(-n) )
P = (L*0.002)/( 1-(1+0.002)^(-180) )
P = L*(0.002)/(0.30207279974017)
P = L*0.00662092052551
P = 0.00662092052551L
That represents the approximate monthly payment P based on the loan amount L, given the conditions listed above. This is equal to the value of A we found earlier, since that also represents the monthly payment.
Equate the two expressions and solve for L
0.00662092052551L = (L+8456.40)/180
180*0.00662092052551L = L+8456.40
1.1917656945918L = L+8456.40
1.1917656945918L-L = 8456.40
0.1917656945918L = 8456.40
L = 8456.40/0.1917656945918
L = 44097.564050758
L = 44097.56
The amount loaned to Alex to be able to purchase the boat was $44,097.56; this is the purchase price of the boat.
