Calculate simple interest for investments and loans. Problem 1: Lisa invests R5000 at 7.5% for 6 years…

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Calculate simple interest for investments and loans. Problem 1: Lisa invests R5000 at 7.5% for 6 years. Problem 2: Jack buys a car for R120000 with a 20% deposit, loan at 10.5% for 5 years. Find total

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Simple Interest

1. Lisa's investment

Identify the principal amount ( $P$ ), interest rate ( $i$ ), and time ( $n$ ).
$P = \text{R}5\,000$
$i = 7.5\% = 0.075$ per year
$n = 6 \text{ years}$
Calculate the simple interest earned using the formula $I = P \cdot i \cdot n$ .
$I = \text{R}5\,000 \times 0.075 \times 6$ $I = \text{R}2\,250$
Calculate the total value of the investment ( $A$ ) by adding the principal and the interest.
$A = P + I$ $A = \text{R}5\,000 + \text{R}2\,250$ $A = \text{R}7\,250$
The value of Lisa's investment at the end of 6 years is $\boxed{\text{R7 250.00}}$ .

2. Jack's car purchase
Identify the selling price of the car.
Selling Price = R120 000
Calculate the deposit amount (20% of the selling price).
$\text{Deposit} = \text{R}120\,000 \times 0.20$ $\text{Deposit} = \text{R}24\,000$
Calculate the loan amount (principal $P$ ) after the deposit.
$\text{Loan Amount} = \text{Selling Price} - \text{Deposit}$ $\text{Loan Amount} = \text{R}120\,000 - \text{R}24\,000$ $\text{Loan Amount} = \text{R}96\,000$
Calculate the simple interest on the loan amount.
$P = \text{R}96\,000$
$i = 10.5\% = 0.105$ per year
$n = 5 \text{ years}$
$I = P \cdot i \cdot n$ $I = \text{R}96\,000 \times 0.105 \times 5$ $I = \text{R}50\,400$
Calculate the total amount Jack pays for the car (Deposit + Loan Amount + Interest on Loan).
$\text{Total Paid} = \text{Deposit} + \text{Loan Amount} + \text{Interest on Loan}$ $\text{Total Paid} = \text{R}24\,000 + \text{R}96\,000 + \text{R}50\,400$ $\text{Total Paid} = \text{R}170\,400$
The total amount Jack pays for the car is $\boxed{\text{R170 400.00}}$ .

Compound Interest

1. R130 000 investment
$P = \text{R}130\,000$
Annual interest rate = 12% = 0.12
Time ( $n$ ) = 3 years
Compounded annually.

a) Calculate the total interest earned.
Calculate the future value ( $A$ ) using the compound interest formula $A = P(1 + i)^n$ .
$A = \text{R}130\,000(1 + 0.12)^3$ $A = \text{R}130\,000(1.12)^3$ $A = \text{R}130\,000 \times 1.404928$ $A = \text{R}182\,640.64$
Calculate the total interest earned ( $I = A - P$ ).
$I = \text{R}182\,640.64 - \text{R}130\,000$ $I = \text{R}52\,640.64$
The total interest earned is $\boxed{\text{R52 640.64}}$ .

b) Determine the value of the investment after three years.
The value of the investment after three years is the future value calculated in part (a).
The value of the investment after three years is $\boxed{\text{R182 640.64}}$ .

2. Jason's R400 000 investment
$P = \text{R}400\,000$
Time = 1.5 years
Annual interest rate = 10% = 0.10
Compounded quarterly.

a) Determine the value of the investment after 1.5 years.
Determine the interest rate per compounding period ( $i$ ) and the total number of compounding periods ( $n$ ).
Since it's compounded quarterly, there are 4 compounding periods per year.
$i = \frac{\text{Annual Rate}}{\text{Number of Compounding Periods per Year}} = \frac{0.10}{4} = 0.025$ $n = \text{Years} \times \text{Number of Compounding Periods per Year} = 1.5 \times 4 = 6 \text{ periods}$
Calculate the future value ( $A$ ) using the compound interest formula $A = P(1 + i)^n$ .
$A = \text{R}400\,000(1 + 0.025)^6$ $A = \text{R}400\,000(1.025)^6$ $A = \text{R}400\,000 \times 1.159693418$ $A = \text{R}463\,877.37$
The value of the investment after 1.5 years is $\boxed{\text{R463 877.37}}$ .

b) What is the total amount of interest earned?
Calculate the total interest earned ( $I = A - P$ ).
$I = \text{R}463\,877.37 - \text{R}400\,000$ $I = \text{R}63\,877.37$
The total amount of interest earned is $\boxed{\text{R63 877.37}}$ .

Calculate simple interest for investments and loans. Problem 1: Lisa invests R5000 at 7.5% for 6 years. Problem 2: Jack buys a car for R120000 with a 20% deposit, loan at 10.5% for 5 years. Find total

Step-by-step solution

Simple Interest

Identify the principal amount ( $P$ ), interest rate ( $i$ ), and time ( $n$ ).

Calculate the simple interest earned using the formula $I = P \cdot i \cdot n$ .

Calculate the total value of the investment ( $A$ ) by adding the principal and the interest.

Identify the selling price of the car.

Calculate the deposit amount (20% of the selling price).

Calculate the loan amount (principal $P$ ) after the deposit.

Calculate the simple interest on the loan amount.

Calculate the total amount Jack pays for the car (Deposit + Loan Amount + Interest on Loan).

Compound Interest

Calculate the future value ( $A$ ) using the compound interest formula $A = P(1 + i)^n$ .

Calculate the total interest earned ( $I = A - P$ ).

Determine the interest rate per compounding period ( $i$ ) and the total number of compounding periods ( $n$ ).

Calculate the future value ( $A$ ) using the compound interest formula $A = P(1 + i)^n$ .

Calculate the total interest earned ( $I = A - P$ ).

Still stuck on this one?

More Mathematics Questions

Calculate simple interest for investments and loans. Problem 1: Lisa invests R5000 at 7.5% for 6 years. Problem 2: Jack buys a car for R120000 with a 20% deposit, loan at 10.5% for 5 years. Find total

Step-by-step solution

Simple Interest

Identify the principal amount (PPP), interest rate (iii), and time (nnn).

Calculate the simple interest earned using the formula I=P⋅i⋅nI = P \cdot i \cdot nI=P⋅i⋅n.

Calculate the total value of the investment (AAA) by adding the principal and the interest.

Identify the selling price of the car.

Calculate the deposit amount (20% of the selling price).

Calculate the loan amount (principal PPP) after the deposit.

Calculate the simple interest on the loan amount.

Calculate the total amount Jack pays for the car (Deposit + Loan Amount + Interest on Loan).

Compound Interest

Calculate the future value (AAA) using the compound interest formula A=P(1+i)nA = P(1 + i)^nA=P(1+i)n.

Calculate the total interest earned (I=A−PI = A - PI=A−P).

Determine the interest rate per compounding period (iii) and the total number of compounding periods (nnn).

Calculate the future value (AAA) using the compound interest formula A=P(1+i)nA = P(1 + i)^nA=P(1+i)n.

Calculate the total interest earned (I=A−PI = A - PI=A−P).

Still stuck on this one?

More Mathematics Questions

Identify the principal amount ( $P$ ), interest rate ( $i$ ), and time ( $n$ ).

Calculate the simple interest earned using the formula $I = P \cdot i \cdot n$ .

Calculate the total value of the investment ( $A$ ) by adding the principal and the interest.

Calculate the loan amount (principal $P$ ) after the deposit.

Calculate the future value ( $A$ ) using the compound interest formula $A = P(1 + i)^n$ .

Calculate the total interest earned ( $I = A - P$ ).

Determine the interest rate per compounding period ( $i$ ) and the total number of compounding periods ( $n$ ).

Calculate the future value ( $A$ ) using the compound interest formula $A = P(1 + i)^n$ .

Calculate the total interest earned ( $I = A - P$ ).