QuestionCompare the future amounts $(A)$ you would have if the money were invested at simple interest and if it were invested with annual compounding. (Rou $\$ 7,600$ at $13 \%$ for 30 years simple interest $A=\$ 37240$ $\square$ Great! compound interest $A=\$$ $\square$ Suggested tutorials:

Studdy Solution

STEP 1

1. The principal amount is \$7,600.
2. The interest rate is 13% per annum.
3. The investment period is 30 years.
4. We need to compare the future amounts using simple interest and compound interest.

STEP 2

1. Calculate the future amount using simple interest.
2. Calculate the future amount using compound interest.
3. Compare the two future amounts.

STEP 3

For simple interest, the formula is: $A = P(1 + rt)$ where $P$ is the principal, $r$ is the rate of interest per year, and $t$ is the time in years.
Given: $P = 7,600$ $r = 0.13$ $t = 30$
Substitute the values into the formula: $A = 7,600(1 + 0.13 \times 30)$
Calculate: $A = 7,600(1 + 3.9)$ $A = 7,600 \times 4.9$ $A = 37,240$

STEP 4

For compound interest, the formula is: $A = P(1 + r)^t$
Substitute the given values: $A = 7,600(1 + 0.13)^{30}$
Calculate: $A = 7,600(1.13)^{30}$
Use a calculator to find $(1.13)^{30}$ : $(1.13)^{30} \approx 37.339$
Now, calculate the future amount: $A = 7,600 \times 37.339$ $A \approx 283,776.40$

STEP 5

Compare the future amounts: - Simple Interest: \$37,240 - Compound Interest: \$283,776.40
The compound interest amount is significantly higher than the simple interest amount.
The future amount with compound interest is approximately:
$\boxed{283,776.40}$

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