Questions: The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value, A, or the total amount due at time t. P=4000, r=6.5%, t=9 months

The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value, A, or the total amount due at time t.
P=4000, r=6.5%, t=9 months

Transcript text: The principal $P$ is borrowed at simple interest rate r for a period of time $t$. Find the loan's future value, A , or the total amount due at time t . \[ \mathrm{P}=\$ 4000, \mathrm{r}=6.5 \%, \mathrm{t}=9 \text { months } \]

Solution

Solution Steps

Step 1: Convert the interest rate from a percentage to a decimal

The interest rate $r$ is given as 6.5\%. We convert it to a decimal by dividing by 100: $r = 0.065$.

Step 2: Convert the time to years if necessary

The time $t$ is given in months. We convert it to years: $t = 0.75$ years.

Step 3: Use the formula $A = P(1 + rt)$ to calculate the future value

Substituting the values into the formula, we get $A = 4000(1 + 0.065 \times 0.75) = 4195$.

Final Answer:

The future value of the loan or investment is $4195$.

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