Simple Interest
What is the definition of “simple interest”?
Interest earned or paid only on the original sum of money that was borrowed or invested
What is the definition of “compound interest”?
When interest is calculated not only on the initial principal but also on the accumulated interest from previous compounding periods
What is the definition of “future value”?
Total amount of an investment after a certain length of time
What is the definition of “present value”?
Principal that would have to be invested now to get a specific future value in a certain amount of time
What is the definition of “principal”?
A sum of money that is borrowed or invested
What is the formula for calculating simple interest?
I = Prt (Interest = Principal x Rate x Time)
What is one of the two formulas for calculating compound interest?
I = A - P
I = P[(1+i)n - 1]
What is the formula for calculating future value?
A = P(1 + i)n
What is one of the two formulas for calculating present value?
PV = A / (1 + i)n
PV = A(1+i)-n
What is the definition of “interest”?
The money earned from an investment or the cost of borrowing money
Naomi invests $850 at 7%/a simple interest. How long will she have to leave her investment in the bank before earning $200 in interest?
T = I / Pr
T = 200 / 850 x 0.07
T = approx. 3 years
Naomi invests $10,000 at 7.2%/a compounded monthly. How long will it take for her investment to grow to $25,000?
A = P(1 + i)n
25,000 = 10,000(1 + 0.072/12)n
2.5 = 1.006n
n = approx. 12 years and 10 months
Naomi bought a $1000 Canada Savings Bond that earns 5%/a compounded annually. She can redeem the bond in 7 years. Determine the future value of the bond.
A = P(1 + r)n
A = 1000(1 + 0.05)7
A = $1407.10
Naomi borrows some money at 7.2%/a compounded annually. After 5 years, she repays $12,033.52 for the principal and the interest. How much money did Naomi borrow?
PV = A / (1 + i)n
PV = 12,033.52 / (1 + 0.072)5
PV = approx. $8500
What is the definition of “interest rate”?
Percentage charged or earned on the principal amount over a certain period
Alexis has a balance of $2845 on her credit card. What rate of simple interest is she being charged if she must pay $26.19 interest for the 12 days her payment is late?
R = I / Pt
R = 26.19 / (2845 x 12/365)
R = approx. 28%
Alexis borrows $5300 at 4.6%/a compounded annually. How much will she have to pay back if she borrows the money for 10 years?
A = P(1 + i)n
A = 5300(1 + 0.046)10
A = approx. $8309.84
Alexis deposits $9000 into an account that pays 10%/a compounded quarterly. After three years, the interest rate changes to 9%/a compounded semi-annually. Calculate the value of his investment two years after this change.
A1= P(1 + i)n
A1= 9000(1 + 0.10/4)3x4
A1= $12,104
A2= 12,104(1 + 0.09/2)2x2
A2= $14,434.24
Alexis saved $900 to buy a plasma TV. She borrowed the rest at an interest rate of 18%/a compounded monthly. Two years later, she paid $1429.50 for the principal and the interest. How much did the TV originally cost?
PV = A / (1 +i)n
PV = 1429.50 / (1 + 0.18/12)2x12
PV =1000 + 900
Cost of TV = $1900
What is the definition of “compounding period“?
Intervals at which interest is calculated
Ms. Gharakhanian invests $5200 at 3%/a simple interest, while Rodas invests $3600 at 5%/a simple interest. How long will it take for Rodas’ investment to be worth more than Ms. Gharakhanian’s?
Approx. more than 66 years
If Rodas’ initial investment of $8000 grows to $12,000 in 5 years with interest compounded quarterly, what is the annual interest rate?
A = P(1+ i)n
12,000 = 8000(1 + r/4)5x4
r = approx. 8%
On July 1, 1996, Rodas invested $2000 in an account that earned 6%/a compounded monthly. On July 1, 2001, she moved the total amount to a new account that paid 8%/a compounded quarterly. Determine the balance in her account on January 1, 2008.
A1= P(1 + i)n
A1= 2000(1 + 0.06/12)5x12
A1= $2697.70
A2= 2697.70(1 + 0.08/4)6.5x4
A2 = $4514.38
Rodas is investing $2500 that she would like to grow to $6000 in 10 years. At what annual interest rate, compounded quarterly, must Rodas invest her money?
PV = A / (1 + i)n
2500 = 6000 / (1 + i)10x4
i = 0.02212
4i = approx. 8.85%
What are the four types of compounding periods?
Annually (one time per year)
Semi-annually (two times per year)
Quarterly (four times per year)
Monthly (twelve times per year)