47.8k views
2 votes
Sutton deposited

$
7500
into an account paying
6.24
%
annual interest compounded monthly. How much money will be in the account after
7
years? (also called Future value).

2 Answers

2 votes

Answer:

Step-by-step explanation:

User Jacob Abraham
by
8.8k points
4 votes

Final Answer:

The future value (FV) of Sutton's deposit of $7500 into an account with a 6.24% annual interest rate compounded monthly after 7 years is approximately $11,407.88.

Step-by-step explanation:

To calculate the future value, we use the compound interest formula:


\[FV = P \left(1 + (r)/(n)\right)^(nt)\]

Where:

  • FV is the future value of the investment/loan.
  • P is the principal amount (initial deposit or loan amount).
  • r is the annual interest rate (as a decimal).
  • n is the number of times that interest is compounded per unit
    \(t\).
  • t is the time the money is invested or borrowed for in years.

In this case:


\(P = $7500\)


\(r = 6.24\% = 0.0624\) (converted to decimal)


\(n = 12\) (compounded monthly)


\(t = 7\) years

Substitute these values into the formula:


\[FV = 7500 \left(1 + (0.0624)/(12)\right)^((12 * 7))\]

Calculate the expression:


\[FV \approx 7500 \left(1 + 0.0052\right)^(84)\]


\[FV \approx 7500 * 1.5017962\]


\[FV \approx 11,407.88\]

Therefore, after 7 years, Sutton's deposit will grow to approximately $11,407.88. This calculation takes into account the compounded interest, resulting in the final future value of the deposit.

User Tharaka Arachchige
by
8.9k points
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