Answer:
Explanation:
We can use the formula for continuous compounding to determine how long it will take each account to reach $1,800.
For Michael's account, the formula is:
A = P*e^(rt)
where:
A is the amount in the account after t years
P is the principal
r is the annual interest rate
t is the time in years
Plugging in the values given, we get:
1,800 = 1,000*e^(0.0475t)
Taking the natural logarithm of both sides, we get:
ln(1,800/1,000) = 0.0475t
t = ln(1,800/1,000)/0.0475
t ≈ 8.55 years
So it will take approximately 8.55 years for Michael's account to reach $1,800.
Similarly, for Peter's account, the formula is:
A = P*e^(rt)
where:
A is the amount in the account after t years
P is the principal
r is the annual interest rate
t is the time in years
Plugging in the values given, we get:
1,800 = 1,200*e^(0.0425t)
Taking the natural logarithm of both sides, we get:
ln(1,800/1,200) = 0.0425t
t = ln(1,800/1,200)/0.0425
t ≈ 9.03 years
So it will take approximately 9.03 years for Peter's account to reach $1,800.
Therefore, Michael's account will grow to $1,800 first as it will take less time (8.55 years) compared to Peter's account (9.03 years).