Question

Kiran plans to save $200 per year. Bank A would pay 6% interest, and bank B would pay 4% interest (both compounded annually). How many years will it take to save $10,000 if he uses bank A? Bank B? Ron’s to the nearest whole number

Answer 1

To save $10,000 using bank A, it will take approximately 18.4 years. To save $10,000 using bank B, it will take approximately 21.9 years.

Step-by-step explanation:

To calculate how many years it will take to save $10,000 using bank A and bank B, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the principal amount (initial deposit), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

For bank A, P = $200, r = 0.06, n = 1 (compounded annually), and we want to find t.

Substituting these values into the formula, we get 10,000 = 200(1 + 0.06/1)^(1t).

Simplifying the equation, we get (1.06)^t = 10000/200 = 50.

Taking the natural logarithm of both sides, we get t × ln(1.06) = ln(50), and solving for t, we find t ≈ 18.4 years.

For bank B, we repeat the same process using P = $200, r = 0.04, and n = 1, and we find that it will take approximately 21.9 years to save $10,000.

Answer 2

It will take approximately 11 years for Kiran to save $10,000 using bank A and approximately 13 years using bank B.

Step-by-step explanation:

To find out how many years it will take for Kiran to save $10,000 using bank A and bank B, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the future value, P is the principal (initial amount saved), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

For bank A, we have:

A = $10,000, P = $200, r = 0.06, and n = 1 (since it is compounded annually).

Plugging in these values, we get:

$10,000 = $200(1 + 0.06/1)^(1t)

Simplifying the equation:

50 = (1.06)^t

Using logarithms, we can solve for t:

t = log(50)/log(1.06)

Calculating this value gives us:

t ≈ 11.896 years

Therefore, it will take approximately 11 years for Kiran to save $10,000 using bank A.

For bank B, we have:

A = $10,000, P = $200, r = 0.04, and n = 1.

Plugging in these values and using the same process as before, we find that it will take approximately 13 years for Kiran to save $10,000 using bank B.