Simple Interest Question

[turtlebanana]

The recurrence relation formula for simple interest is Vn+1 = Vn + d where d = Vo x r / 100

The d calculates the amount of interest earned per period. But my question is - is it only for simple interest?
Could you do it for compound interest as well?

For the following question:
Lucy wants to borrow $25000. Interest is calculated and compounded quarterly on the reducing balance at an interest rate of 7.9% p.a.
a) If Lucy can afford to repay her loan at $1600 quarter, then how much of Lucy's first payment goes towards paying the interest?
The solution uses the formula d = Vo x r/100 --> d = 25000 x 7.9/4/100 = $493.75
The question says it is ''compounded quarterly'' so it is definitely not simple interest.
Does that mean i can use the formula d = Vo x r/100  to calculate the amount of interest earned per period for simple as well as compound interest? I imagine not because this formula gives a flat interest rate, whereas compounding interest on a reducing balance loan means the interest decreases with each successive payment..

So confused.. Then why did the solutions use it for this question?

[S_R_K]

The recurrence relation formula for simple interest is Vn+1 = Vn + d where d = Vo x r / 100

The d calculates the amount of interest earned per period. But my question is - is it only for simple interest?
Could you do it for compound interest as well?

For the following question:
Lucy wants to borrow $25000. Interest is calculated and compounded quarterly on the reducing balance at an interest rate of 7.9% p.a.
a) If Lucy can afford to repay her loan at $1600 quarter, then how much of Lucy's first payment goes towards paying the interest?
The solution uses the formula d = Vo x r/100 --> d = 25000 x 7.9/4/100 = $493.75
The question says it is ''compounded quarterly'' so it is definitely not simple interest.
Does that mean i can use the formula d = Vo x r/100  to calculate the amount of interest earned per period for simple as well as compound interest? I imagine not because this formula gives a flat interest rate, whereas compounding interest on a reducing balance loan means the interest decreases with each successive payment..

So confused.. Then why did the solutions use it for this question?

Suppose that $P is borrowed, and this incurs r% interest per compounding period. In that case, the amount of interest earned for the first compounding period will be r% of P. This is exactly the same as calculating r% simple interest of P, because for the first compounding period, the principal has not yet accrued any interest. For the remaining compounding periods, you can not calculate the amount of interest earned (or paid off) in that period by calculating r% of P.

[plato]

Lucy wants to borrow $25000. Interest is calculated and compounded quarterly on the reducing balance at an interest rate of 7.9% p.a.
a) If Lucy can afford to repay her loan at $1600 quarter, then how much of Lucy's first payment goes towards paying the interest?
The solution uses the formula d = Vo x r/100 --> d = 25000 x 7.9/4/100 = $493.75
The question says it is ''compounded quarterly'' so it is definitely not simple interest.
Does that mean i can use the formula d = Vo x r/100  to calculate the amount of interest earned per period for simple as well as compound interest?

A recurrence relation uses a value to calculate the next value in a sequence.
Your question asks only about the FIRST repayment so compounding has not yet had any effect and the quarterly rate is applied only to the initial value. So this calculation will look like a simple interest calculation. For all subsequent repayments, interest will no longer be calculated on the initial value. Of course the compound interest formula could be used instead if recurrence is not required. The CI formula uses an initial value to calculate some designated future value.