Question

A woman invests $6300 in an account that pays 6% interest per year, compounded continuously (a) What is the amount after 3 years? (Round your answer to the nearest cent:) $/7542.47 (b) How long will it take for the amount to be $11,000?

Answer 1

The answer to part A of this problem is $7542.46938 whereas the answer of part B is 9.289077322 years

As per the formula of Amount :

Amount = Principle × eˣᵇ

Principle = 6300

X (rate of interest) = 6% = 0.06

b (Time period) = 3 years

e = exponent(use calculator)

Amount = 6300 × e^(0.06) × (3)

Amount = 6300 × e^0.18 = 6300×1.1972173=$7542.46938

2. Using the same formula: Amount = Principle × eˣᵇ

Given Amount = $11000

11,000 = 6300 × e^(0.06) × (b)

e^0.06 × b = 11000/6300 = 1.74603

log 1.74603 = log(e^0.06×b)

= 0.242051/0.06 = log(e^b)

4.034195 = log e^b

b = 4.034195/log e (use calculator)

= 9.289077322

b = 9.289077322 years