This question is incomplete. Below is the complete question:
A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were made. At the end of an 8 year period, the balance in the account was $13231.30. what is the amount of the initial deposit?
Answer: The initial deposit is $10,001
Step-by-step explanation:
To solve this we need to utilize the continuous compounding interest formula:-
Fv = Pv × e^(i × t)
Where, Fv = the future value
Pv = present value
i = the interest rate
t = the time in years
e = a mathematical constant that is usually approximated by 2.7183
In this case, the Fv = 13,231.30
i = 3.5% or 0.035
t = 8 years
e = 2.7183
Pv = ? (The unknown variable).
13,231.30 = Pv × [2.7183^(0.035 × 8)]
13,231.30 = Pv × [2.7183^(0.28)]
13,231.30 = Pv × 1.323
Pv = 13,231.30/1.323
Pv = $10000.98
= $10,001
Therefore the initial deposit is $10,001
