Suppose there is a new kind of savings certificate that starts out paying 3.5% annual interest and increases the interest rate by 1% each additional year that the money is left on deposit.(Assume that interest is compounded continuously and that the interest rate increases continuously.)Assuming an initial deposit of $1500, which of the following investment choices is better?
A)Investing the money at a fixed interest rate of 5% for 4 years.
B)Investing the money in the new kind of savings certificate for 4 years.

Question

Quizplus · Accepted Answer

The new savings certificate offers a continuously increasing interest rate, starting at 3.5% and increasing by 1% each year. This means the average interest rate over the 4 years will be higher than the starting rate and will exceed the fixed 5% rate offered in option A. Given the power of compound interest, especially with an increasing rate, the total return from the savings certificate will surpass the return from a fixed 5% interest rate over the same period.

Suppose There Is a New Kind of Savings Certificate That