Midterm Study Sheet - Side-by-Side
Format (Expanded)
Simple Interest Compound Interest
Formula: I = P × r × t Formula: A = P × (1 + r/n)^(n × t)
Where: Where:
I = Interest A = Accumulated amount
P = Principal P = Principal
r = Annual interest rate (decimal) r = Annual rate
t = Time in years n = Compounds/year
Example: $1,325 at 8.5% for 90 days t = Years
t = 90/360 → I = 1325 × 0.085 × 0.25 = Example: $500 at 6% quarterly for 5 yrs →
$28.16 A ≈ $552.45
Present Value Percent Change
Formula: P = A / (1 + r/n)^(n × t) Formula: % Change = (New - Original) /
Example: $150,000 in 2 yrs at 8% quarterly Original × 100
→ P ≈ $128,023.56 Example: 500 → 545 → (45/500)×100 = 9%
APY Calculation Installment Loan Payment
Formula: APY = (1 + r/n)^n - 1 Formula: m = P × (r/n) / [1 - (1 + r/n)^(-n ×
Example: 2.2% monthly → APY ≈ 2.22% t)]
Round UP to nearest half percent in tables. Example: $35,000, 4 yrs, 7.5% → m ≈
$846.26
Finance Charge Down Payment and Points
Formula: FC = Total Paid - Amount Down = Home × %
Financed Points = Loan × % (1 point = 1%)
Example: $12,521.28 - $11,000 = Ex: 20% of $715k = $143k, 1 pt on $175k =
$1,521.28 $1,750
Ordinary Annuity Sinking Fund
Formula: FV = PMT × [(1 + r)^n - 1] / r Formula: PMT = A × (r/n) / [(1 + r/n)^(n × t) -
Example: $5,000/yr, 6%, 3 yrs → FV ≈ 1]
$15,918.00 Ex: $230,000 in 29 yrs at 6% monthly →
PMT ≈ $246.11
Modular Arithmetic Base-n Systems
Mod refers to the remainder after division. Each digit's place is a power of the base.
Used in cycles like clocks and calendars. Read by multiplying each digit by
Formula: a mod m = remainder when a is base^position.
divided by m Example: 615₇ = 6×49 + 1×7 + 5 = 306
Example: (2 + 167) mod 7 = 169 mod 7 = 1 Convert base-10 to base-n: Divide by base
→ Monday repeatedly.
Another example: 55 months from
Format (Expanded)
Simple Interest Compound Interest
Formula: I = P × r × t Formula: A = P × (1 + r/n)^(n × t)
Where: Where:
I = Interest A = Accumulated amount
P = Principal P = Principal
r = Annual interest rate (decimal) r = Annual rate
t = Time in years n = Compounds/year
Example: $1,325 at 8.5% for 90 days t = Years
t = 90/360 → I = 1325 × 0.085 × 0.25 = Example: $500 at 6% quarterly for 5 yrs →
$28.16 A ≈ $552.45
Present Value Percent Change
Formula: P = A / (1 + r/n)^(n × t) Formula: % Change = (New - Original) /
Example: $150,000 in 2 yrs at 8% quarterly Original × 100
→ P ≈ $128,023.56 Example: 500 → 545 → (45/500)×100 = 9%
APY Calculation Installment Loan Payment
Formula: APY = (1 + r/n)^n - 1 Formula: m = P × (r/n) / [1 - (1 + r/n)^(-n ×
Example: 2.2% monthly → APY ≈ 2.22% t)]
Round UP to nearest half percent in tables. Example: $35,000, 4 yrs, 7.5% → m ≈
$846.26
Finance Charge Down Payment and Points
Formula: FC = Total Paid - Amount Down = Home × %
Financed Points = Loan × % (1 point = 1%)
Example: $12,521.28 - $11,000 = Ex: 20% of $715k = $143k, 1 pt on $175k =
$1,521.28 $1,750
Ordinary Annuity Sinking Fund
Formula: FV = PMT × [(1 + r)^n - 1] / r Formula: PMT = A × (r/n) / [(1 + r/n)^(n × t) -
Example: $5,000/yr, 6%, 3 yrs → FV ≈ 1]
$15,918.00 Ex: $230,000 in 29 yrs at 6% monthly →
PMT ≈ $246.11
Modular Arithmetic Base-n Systems
Mod refers to the remainder after division. Each digit's place is a power of the base.
Used in cycles like clocks and calendars. Read by multiplying each digit by
Formula: a mod m = remainder when a is base^position.
divided by m Example: 615₇ = 6×49 + 1×7 + 5 = 306
Example: (2 + 167) mod 7 = 169 mod 7 = 1 Convert base-10 to base-n: Divide by base
→ Monday repeatedly.
Another example: 55 months from
