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

It will take approximately 67 years for Kiran to save $10,000 with a 6% interest rate in Bank A and around 100 years with a 4% interest rate in Bank B.

To determine how many years it will take Kiran to save $10,000 with compound interest, we can use the compound interest formula:

`\[A = P \left(1 + (r)/(n)\right)^(nt)\]`

where:

- A is the future value of the investment,

- P is the principal amount (initial deposit),

- r is the annual interest rate (in decimal form),

- n is the number of times interest is compounded per year,

- t is the number of years.

For Bank A:

`\[10,000 = 200 * (1.06)^t\]`

`\[50 = (1.06)^t\]`

`\[t = (\log(50))/(\log(1.06)) \approx 67.13\]`

For Bank B:

`\[10,000 = 200 * (1.04)^t\]\[50 = (1.04)^t\]\[t = (\log(50))/(\log(1.04)) \approx 99.74\]`

The results indicate that it will take approximately 67.13 years for Kiran to save $10,000 using Bank A and approximately 99.74 years using Bank B.

The complete question is:

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? Round to the nearest whole number