Let’s solve each problem step by step using the simple interest formula:
Simple Interest (I) = Principal × Rate × Time
Amount (A) = Principal + Interest
Remember:
- Rate must be in decimal form (so 5% = 0.05, 8% = 0.08, etc.)
- Time is in years
- All answers should be in dollars ($)
---
A) Find I and A for each:
#### 1) Principal = $13,700, Time = 2 years, Rate = 5% per annum
→ Convert rate: 5% = 0.05
→ I = 13700 × 0.05 × 2 = 13700 × 0.10 =
$1,370
→ A = 13700 + 1370 =
$15,070
✔ Check: 5% of 13700 is 685 per year → 685 × 2 = 1370 ✔️
---
#### 2) Principal = $9,800, Time = 6 years, Rate = 8% per annum
→ Rate = 0.08
→ I = 9800 × 0.08 × 6 = 9800 × 0.48
Let’s compute:
9800 × 0.48 = (9800 × 0.50) - (9800 × 0.02) = 4900 - 196 =
$4,704
→ A = 9800 + 4704 =
$14,504
✔ Check: 8% of 9800 = 784 per year → 784 × 6 = 4704 ✔️
---
#### 3) Principal = $5,425, Time = 5 years, Rate = 13% per annum
→ Rate = 0.13
→ I = 5425 × 0.13 × 5 = 5425 × 0.65
Compute:
5425 × 0.65 = 5425 × (0.60 + 0.05) = (5425×0.60) + (5425×0.05)
= 3255 + 271.25 =
$3,526.25
→ A = 5425 + 3526.25 =
$8,951.25
✔ Check: 13% of 5425 = 705.25 per year → 705.25 × 5 = 3526.25 ✔️
---
#### 4) Principal = $400, Time = 10 years, Rate = 2% per annum
→ Rate = 0.02
→ I = 400 × 0.02 × 10 = 400 × 0.20 =
$80
→ A = 400 + 80 =
$480
✔ Check: 2% of 400 = 8 per year → 8 × 10 = 80 ✔️
---
B) Total amount payable on $700 at end of 4 years
#### a) At 11% simple interest per year
→ I = 700 × 0.11 × 4 = 700 × 0.44 =
$308
→ A = 700 + 308 =
$1,008
✔ Check: 11% of 700 = 77 per year → 77 × 4 = 308 ✔️
#### b) At 4% simple interest per year
→ I = 700 × 0.04 × 4 = 700 × 0.16 =
$112
→ A = 700 + 112 =
$812
✔ Check: 4% of 700 = 28 per year → 28 × 4 = 112 ✔️
---
Final Answer:
A)
1) I = $1,370; A = $15,070
2) I = $4,704; A = $14,504
3) I = $3,526.25; A = $8,951.25
4) I = $80; A = $480
B)
a) $1,008
b) $812
Parent Tip: Review the logic above to help your child master the concept of simple interest worksheet answer key.
