Question

How much money invested at 5% compounded continuously for 3 years will yield $820?

Answer 1

Percentage of interest at which the money is invested = 5%
Time for which the money is invested = 3 years
The final amount after 3 years = $820
Let us assume the principal amount = x dollars
Then
820 = x (1 + 0.5)^3
820 = x(1.05)^3
x = 820/(1.05)^3
   = 708.35 dollars
From the above deduction, we can conclude that the principal amount invested was $708.35.

Answer 2

To solve for compounding continuously follow the equation:

A = Pe^rt

A = Amount

P = Principal

e = Constant e

r = Rate of interest

t = Time in years

What we know:

Interest rate in percent = 5%

Length of time money is invested = 3 years

Total after 3 years = $820

What we want to know: amount of money that will yield $820 after 3 years at a 5% interest rate = X

To solve:

820 = X(1 + 0.5)^3

820 = X(1.05)^3

X = 820/(1.05)^3

X = 708.35 dollars

The principal amount invested was $708.35