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.

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