Question

Suppose when you are 21 years old, you deposit $1,000 into a bank account thatpays annual compound interest, and you do not withdraw from the account untilyour retirement at the age of 65, 44 years later. How much more will be in youraccount if the interest rate is 6 percent rather than 5 percent?

Answer 1

Answer:

The difference between the two rates is $4,428.33.

Explanation:

When the interest is compounded, it is calculated over the value of the investment at the end of the previous year. So, value at year 1 will be 1,000*(1+rate). At second, it will be 1,000*(1+rate)*(1+rate), or 1,000 * (1+rate)^2.

If we extend the analysis, at year 44, the investment will be worth 1,000*(1+r)^44.

If rate is 5 percent, the result of the deposit is 1,000*1.05^44 = 8,557.15

If rate is 6 percent, the result of the deposit is 1,000*1.06^44 = 12,985.48

The difference is 4,428.33.