Applying logarithm to evaluate T.644204=400000(1+10%)?

To solve for T, we can use the formula for compound interest:

T = P(1 + r)^n

Where:
T = Total amount
P = Principal amount (initial investment)
r = Interest rate
n = Number of compounding periods

Given:
P = 400000
r = 10% = 0.10
n = 1

Substitute the values into the formula:

T = 400000(1 + 0.10)^1
T = 400000(1.10)
T = 440000

Therefore, the total amount after one compounding period is $440,000.

Given T.644204 = 400000(1 + 10%)^_?

Taking log on both sides, we get:

log T.644204 = log 400000 + log (1 + 10%)^_?

=> log T.644204 = log 400000 + _? log (1 + 10%)

=> log T.644204 = 5.6021 + _? log 1.1

=> log T.644204 = 5.6021 + _? (0.0414)

=> log T.644204 = 5.6021 + 0.0207

=> log T.644204 = 5.6228

=> T.644204 = 10^5.6228

Therefore, T = 4144204