Natasha's Mortgage Adventure!
How many payments will Natasha have to make to repay the mortgage?
Natasha bought a house with a mortgage of $307,000. The mortgage is being financed with an interest rate of 5.36% compounded monthly. Natasha will make payments of $2,477. How many payments will Natasha have to make to repay the mortgage?
Answer:
While Natasha has to make payments to repay the mortgage of $307,000 with an interest rate of 5.36% compounded monthly and making payments of $2,477, she shall have to make 253 payments.
Explanation:
We'll use the mortgage payment formula:
N = -(log(1 - (r * P) / M) / log(1 + r))
Where:
N = number of payments
P = principal (mortgage amount) = $307,000
r = monthly interest rate = 0.0536 / 12 = 0.00447
M = monthly payment amount = $2,477
1. Plug the values into the formula:
N = -(log(1 - (0.00447 * 307,000) / 2,477) / log(1 + 0.00447))
2. Calculate the expression inside the parentheses:
(0.00447 * 307,000) / 2,477 = 0.67569
3. Subtract this value from 1:
1 - 0.67569 = 0.32431
4. Calculate the logarithm of the result:
log(0.32431) = -0.48957
5. Calculate the logarithm of (1 + 0.00447):
log(1.00447) = 0.00194
6. Divide the two logarithms:
-0.48957 / 0.00194 = -252.55
Since we cannot have a fraction of a payment, Natasha will need to make 253 payments to repay the mortgage.