Calculate the total savings after a change in interest rate on a loan.

April 11, 2026Mathematics

ScanSolve AI Answer

April 11, 2026

Answer

PMT \times \frac{1 - (1 + i)^{-N}}{i}$$

Another day — let's solve it.

To solve this problem, we need to calculate the original monthly payment, then the new monthly payment after the interest rate change, and finally the difference between the two.

Step 1: Calculate the original monthly payment ( $PMT_1$ )

The formula for the present value of an ordinary annuity is: $PV = PMT \times \frac{1 - (1 + i)^{-N}}{i}$ Where:

$PV$ = Present Value (loan amount) = R911 012.00
$PMT$ = Monthly Payment
$i$ = Monthly interest rate = $\frac{Annual interest rate}{12}$
$N$

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Quick Answer

Another day — let's solve it. To solve this problem, we need to calculate the original monthly payment, then the new monthly payment after the interest rate change, and finally the difference between the two.

Asked on April 11, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 11, 2026

Another day — let's solve it. To solve this problem, we need to calculate the original monthly payment, then the new monthly payment after the interest rate change, and finally the difference between the two. Step 1: Calculate the original monthly payment (PMT_1) The formula for the present value of an ordinary annuity is: PV = PMT × 1 - (1 + i)^-Ni Where: PV = Present Value (loan amount) = R911 012.00 PMT = Monthly Payment i = Monthly interest rate = Annual interest rate12 N