Suppose that in the year 1623 22 was invested at a 5 compoun

Suppose that in the year 1623, $22 was invested at a 5% compound interest rate, compunded quartely. In what year did the balance reach $1000?

Thank you

Solution

in the year 1623, $22 was invested at a 5% compound interest rate, compunded quartely. In what year did the balance reach $1000?

Let time we need to find be t

Principla(P) = $22 ; rate = 5% compunded quartely(r) = 0.05/4 ; Amount(A) = $1000

A = P( 1 +r/400)^t

1000 = 22( 1 + 5/400)^t

4.54 = 1.0125^t

take ln on both sides:

ln( 4.54) = t*ln(1.0125)

t = 121.88

Year = 1745