Step-by-step explanation:
To calculate the interest earned at Bank A, we use the formula for simple interest:
Interest = Principal × Rate × Time
So for Bank A:
Interest = $10,000 × 6.3% × 8 years
For Bank B, we use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (in decimal)
n = the number of times that interest is compounded per unit 't'
t = the time the money is invested for, in years
Here, P = $10,000, r = 4.8% (0.048), n = 1 (compounded annually), and t = 8 years.
So now, we calculate the future value (A) and then subtract the principal to get the compound interest earned.
After calculating both, we find the difference to know how much more interest Rohan will earn by choosing the better offer. Let me do the math.
For Bank A:
Interest = $10,000 × 6.3% × 8 years = $10,000 × 0.063 × 8 = $5,040
For Bank B:
A = $10,000 × (1 + 0.048/1)^(1*8) = $10,000 × (1 + 0.048)^8 ≈ $14,820.88
Compound interest = $14,820.88 - $10,000 = $4,820.88
The difference in interest earned:
$5,040 (Bank A) - $4,820.88 (Bank B) = $219.12
Rohan will earn $219.12 more interest if he invests in Bank A, which offers the better offer.
