Compound Interest with Regular monthly contributions Formula

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I have discover formulas to build Investment Calculator by using compound interest (TVM) concept formula.

The base of the formula

1. Find Future Value: FV= P(1 +r/n) ^ (nt) + PMT * [(((1 + r/n) ^ (nt)) -1 ) / (r/n)]

2. Find Monthly Contribution Amount (PMT): (FV-P(1 +r/n) ^ (nt))/[((1+ r/n) ^ (nt) -1] / (r/n)]

3. Find Initial Investment Amount/Principal (P): (FV-(PMT * [((1 + r/n) ^ (nt) -1 ])/ (r/n)] /((1 +r/n) ^ (nt))

I had research many sources, seems like no formula that can directly to calculate

1. t (number of investment years)
2. r (returns per annum) by shifting this algorithm FV= P(1 +r/n) ^ (nt) + PMT * [(((1 + r/n) ^ (nt)) -1 ) / (r/n)]

i) Anyone has ways to solve t if P = 1,000 r = 5% n = 12 (compound monthly) PMT = 100 (contribute every end of month) FV = 40,000

Find t by re-arrange t=

or any other method?

ii) Anyone has ways to solve r if P = 1,000 t = 10 years n = 12 (compound monthly) PMT = 100 (contribute every end of month) FV = 40,000

Find r by re-arrange r=

or any other method? i have search methods, but stated it only can using trail and error to calculate because of nature of the formula.

Beside, I've been looking for formula to solve it, but only with simple lump sum formula without PMT. Need the experts to help out...had my brain bursting these few days

Thanks!!!!!!❤️❤️❤️❤️

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