Question

Solve the following formula for t.
Upper M equals Upper U left parenthesis 1 plus rt right parenthesis

Answer 1

To solve the formula \( M = U(1 + rt) \) for \( t \), follow these steps:

1. Start with the equation:
\[
M = U(1 + rt)
\]

2. Divide both sides by \( U \) to isolate the term containing \( t \):
\[
\frac{M}{U} = 1 + rt
\]

3. Subtract 1 from both sides:
\[
\frac{M}{U} - 1 = rt
\]

4. To simplify the left side, express \( 1 \) with a common denominator:
\[
\frac{M - U}{U} = rt
\]

5. Finally, divide both sides by \( r \) to solve for \( t \):
\[
t = \frac{\frac{M - U}{U}}{r} = \frac{M - U}{Ur}
\]

Thus, the formula solved for \( t \) is:
\[
t = \frac{M - U}{Ur}
\]