The interest rate of $16,000 investment is 8.6% and the interest rate
of $11,000 investment is 8%
Step-by-step explanation:
The annual interest formula is I = P r t , where
1. P is the money invested
2. r is the interest rate in decimal
3. t is the time
The annual interest rate on $16,000 investment exceed the interest
earned on $11,000 investment by $496 the $16,000 investment at
0.6% higher rate of interest then the $11,000
Assume that $16,000 investment is , the annual interest
rat is and the interest is
Assume that $11,000 investment is , the annual interest
rat is and the interest is
∵ The annual interest rate on $16,000 investment exceed the interest
earned on $11,000 investment by $496
∴ - = 496
∵ = 16,000 ()(1)
∵ = 11,000 ()(1)
- Substitute them in the equation above
∴ 16,000 ()(1) - 11,000 ()(1) = 496
∴ 16,000 () - 11,000 () = 496 ⇒ (1)
∵ The $16,000 investment at 0.6% higher rate of interest then
the $11,000
∴ = + (0.6/100)
∴ = + 0.006 ⇒ (2)
- Substitute equation (2) in equation (1)
∴ 16,000 ( + 0.006) - 11,000 () = 496
∴ 16,000 + 96 - 11,000 = 496
- Subtract 96 from both sides and add like terms in L.H.S
∴ 5,000 = 400
- Divide both sides by 5,000
∴ = 0.08
- Substitute the value of in equation (2)
∴ = 0.08 + 0.006 = 0.086
- Change them to percent by multiply them by 100%
∴ The interest rate of $16,000 investment = 0.086 × 100% = 8.6%
∴ The interest rate of $11,000 investment = 0.08 × 100% = 8%
The interest rate of $16,000 investment is 8.6% and the interest
rate of $11,000 investment is 8%
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