at what interest rate would a deposit of $20000 grow to $29836 in 25 years with continuous compounding?
29836 = 20000 e^(25 r)
ln(29836 / 20000) = 25 r
To find the interest rate at which a deposit of $20,000 would grow to $29,836 in 25 years with continuous compounding, we can use the formula for compound interest:
A = P * e^(rt)
Where:
A = the final amount (in this case, $29,836)
P = the principal amount (initial deposit, in this case, $20,000)
e = Euler's number (approximately 2.71828)
r = the interest rate
t = the time period (in this case, 25 years)
To isolate the interest rate, we can rearrange the formula as follows:
r = ln(A / P) / t
Now we can plug in the given values and calculate the interest rate:
r = ln(29836 / 20000) / 25
r = ln(1.4918) / 25
r ≈ 0.0297
Therefore, the interest rate required for a deposit of $20,000 to grow to $29,836 in 25 years with continuous compounding is approximately 2.97%.