Question

Linda has d dollars in an account that pays 1.4% interest, compounded weekly. She withdraws w dollars. Express her first week’s interest algebraically.

Answer 1

7/26000 * (d - w),

= $ 0.00027(d - w)

Explanation:

Using simple interest equation given by:

I = (P*r*t)/100,

Where,

I = interest

P = principal amount (initial amount)

= initial amount put - final amount

= $ d - $ w,

r = interest rate,

t = time taken,

n = 1

t = 1/52 years (52 weeks in a year)

r = 1.4 %

P = $ d - $ w

Using the first equation,

= (d - w)*1.4*1/52)/100,

= 7/26000 * (d - w),

= $ 0.00027(d - w)

Answer 2

If the 1.4% rate of interest is the weekly rate of interest, Then, total first week interest = 1.4(d - w)/100 = 0.014(d - w)

But if the 1.4% rate of interest is a yearly rate of interest compounded weekly, then her total first week interest = 7(d - w)/2600 = 0.00269 (d - w)

Explanation:

The interest, I = PRT

P = initial amount of dollars in account = (deposit - withdrawal) = (d - w)

R = rate of interest = 1.4% = 0.014/week

T = time = 1 week

If the 1.4% rate of interest is the weekly rate of interest

I = PRT = (d - w) × 0.014 × 1 = 0.014(d - w)

But if the 1.4% rate of interest is a yearly rate if interest compounded weekly,

P = initial amount of dollars in account = (deposit - withdrawal) = (d - w)

R = rate of interest = 1.4% = 0.014/year

T = time = 1 week = (1/52) years

I = PRT = (d - w) × 0.014 × (1/52) = 7(d - w)/2600 = 0.00269 (d - w)

Hope this Helps!!!