Solve the Problem $A ( t ) = P e ^ { r t }$

question 103

Multiple Choice

Solve the problem.
-An investment grows exponentially under continuous compounding. After 2 yr, the amount in the account is $6,962.58. After 5 yr, the amount in the account is $8,089.36. Use the model $A ( t ) = P e ^ { r t }$ to
a. Find the interest rate r. Round to the nearest percent.
b. Find the original principal P. Round to the nearest dollar.
c. Determine the amount of time required for the account to reach a value of $17,000. Round to the
Nearest year.

• A) \(r = 6 \%\);
• \(P = \$ 6,000\);
• \(\mathrm { t } = 17 \mathrm { yr }\)
• B) \(r = 5 \%\);
• \(P = \$ 6,000\);
• \(\mathrm { t } = 21 \mathrm { yr }\)
• C) \(r = 5 \%\);
• \(P = \$ 6,300\);
• \(\mathrm { t } = 20 \mathrm { yr }\)
• D) \(r = 5 \%\);
• \(P = \$ 6,300\);
• \(\mathrm { t } = 19 \mathrm { yr }\)

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Definitions:

Spreadsheet Heading

The title section at the top of a spreadsheet document that typically contains the name of the spreadsheet, columns, rows, or specific data identifiers.

Adjusted Trial Balance

A statement showing all balances of ledger accounts after adjustments, used to prepare financial statements.

Adjustments Column

A column in journals or ledgers where adjustments are made to correct or update account balances before the preparation of financial statements.

Unadjusted

Refers to figures or entries that have not been modified to reflect adjustments, corrections, or changes.