Question
Shania invests $750 at a rate of \(2\frac{1}{2}\) per year simple interest.
Calculate the total amount Shania has after 5 years.
▶️Answer/Explanation
To calculate the total amount Shania has after 5 years with simple interest, we’ll use the formula:
A=P(1+rt)
Where:
A = Total amount after time t
P = Principal amount (initial investment)
r = Interest rate per time period
t = Time in years
P = \($750\) (principal amount)
r = 2.5% = 0.025 (interest rate per year)
t = 5 years
Substituting the values into the formula, we have:
\(A=750(1+0.025\times 5)\)
A=750(1+0.125)
\(A=750\times 1.125\)
A=843.75
Therefore, Shania will have a total of\( $843.75\) after 5 years with simple interest.
Question
Bruce invested $800 at a rate of 3% per year simple interest.
Calculate the total amount he has after 6 years.
▶️Answer/Explanation
To calculate the total amount Bruce has after 6 years with simple interest, we can use the formula:
A=P+P.r.t
where:
A is the total amount,
P is the principal amount (initial investment),
r is the interest rate per year (as a decimal),
t is the time period in years.
Given:
\(P=$800\)
r=3%=0.03
t = 6 years
Plugging in the values into the formula, we get:
A=800+800.0.03.6
A = 800 + 144
\(A=$944\)
Therefore, Bruce will have \($944\) after 6 years with simple interest.
Question
Bruce invested $420 at a rate of 4% per year compound interest
Calculate the total amount Bruce has after 2 years.
Give your answer correct to 2 decimal places.
▶️Answer/Explanation
To calculate the total amount Bruce has after 2 years with compound interest, we can use the formula:
\(A=P(1+r)^{t}\)
where:
A is the total amount,
P is the principal amount (initial investment),
r is the interest rate per year (as a decimal),
t is the time period in years.
Given:
\(P=$420\)
\(r = 4% = 0.04\)
t = 2 years
Plugging in the values into the formula, we get:
\(A=420\left ( 1+0.04 \right )^{2}\)
\(A=420\times 1.04^{2}\)
\(A=420\times 1.0816\)
\(A ≈ $454.94\)
Therefore, Bruce will have approximately \($454.94\) after 2 years with compound interest.
Question
Dominic invests $850 at a rate of 3.5% per year compound interest.
Calculate the total amount he has after 3 years.
▶️Answer/Explanation
To calculate the compound interest, we use the formula:
\(A=P(1+r)^{t}\)
where:
A is the total amount after t years,
P is the principal amount (initial investment),
r is the interest rate per year (as a decimal),
t is the time period in years.
Plugging in the values, we have:
\(A=850\left ( 1+0.035 \right )^{3}\)
\(A=850\left ( 1.035 \right )^{3\)
\(A\approx 850\times 1.107949875\)
\(A\approx $942.41\)
Therefore, after 3 years, Dominic will have approximately\( $942.41\) with compound interest.
Question
To hire a bicycle it costs \($6\) for each day, plus a fixed charge of \($15.\)
(a) Maria pays \($39\) to hire a bicycle.
How many days does she hire it for?
(b) Write down a formula for the cost, C dollars, to hire a bicycle for d days.
▶️Answer/Explanation
(a) Let’s denote the number of days as d.
The cost for hiring a bicycle is $6 per day, plus a fixed charge of $15. So, the total cost can be represented by the equation:
\($6d + $15 = $39\)
\($6d = $39 – $15\)
\($6d = $24\)
d \(=\frac{$24}{$6}\)
d = 4
Therefore, Maria hired the bicycle for 4 days.
(b) The formula for the cost, C dollars, to hire a bicycle for d days can be expressed as:
C = 6d + 15
“C” represents the total cost in dollars,
“d” represents the number of days the bicycle is hired for,
$6 represents the cost per day, and $15 represents the fixed charge.