Final answer:
To have $5000 in a savings account after five years with continuous compounding at a 7% interest rate, approximately $352 should be deposited initially.
Step-by-step explanation:
To find out how much money should be deposited to have $5000 in the account at the end of five years, we can use the formula for compound interest:
A = P * e^(rt)
Where:
- A is the amount of money at the end of the time period
- P is the principal amount (initial deposit)
- e is the base of the natural logarithm (approximately 2.71828)
- r is the interest rate (as a decimal)
- t is the time period in years
Plugging in the given values, we have:
5000 = P * e^(0.07*5)
5000 = P * e^(0.35)
P = 5000 / e^(0.35)
Simplifying further, we find that P is approximately $352. Therefore, the correct answer is D. $352.