1.) 275 = 150(1+x)^16

275/150 = (1+x)^16

Raise both sides to their 1/16th power,

(275/150)^(1/16) = 1+x

1.038610215 = 1 +x

x = 0.038610215 ---------------answer.

Another way, using logarithms:

275 = 150(1+x)^16

275/150 = (1+x)^16

1.833333333 = (1+x)^16

Take the natural logs of both sides, -----(use common logs if you like).

Ln(1.8333333333) = 16Ln(1+x)

0.606135804 = 16Ln(1+x)

Divide both sides by 16,

0.037883488 = Ln(1+x)

e^0.037883488 = 1+x

1.038610215 = 1+x

x = 0.038610215 -----------same as above.

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2) 500 = 100 (1+0.065/2)^n

Here you'd be forced to use logarithms only.

Divide both sides by 100,

5 = (1.0325)^n

Ln(5) = n*Ln(1.0325)

n = Ln(5) / Ln(1.0325)

n = 50.32159601 -----------------answer.