Question

Olivia invested $110 in an account paying an interest rate of 8 3/4% compounded quarterly. Jai

invested $110 in an account paying an interest rate of 8 5/8% compounded monthly. After 16
years, how much more money would Olivia have in her account than Jai, to the nearest dollar?

Answer 1

Olivia would have approximately $312.73 and Jai would have approximately $313.84 after 16 years. The difference in their accounts would be approximately $1.11.

Step-by-step explanation:

To find the difference in the amount of money Olivia and Jai would have after 16 years, we need to use the compound interest formula.

For Olivia, the principal amount is $110, the interest rate is 8 3/4%, compounded quarterly.

Using the formula A = P(1 + r/n)^(nt), where A is the future amount, P is the principal amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years, we get:

A = 110(1 + 0.0875/4)^(4*16)

= 110(1.021875)^64

≈ $312.73

For Jai, the principal amount is also $110, the interest rate is 8 5/8%, compounded monthly. Using the same formula, we get:

A = 110(1 + 0.08625/12)^(12*16)

= 110(1.0071875)^192

≈ $313.84

So, Olivia would have approximately $312.73 and Jai would have approximately $313.84. The difference in their accounts would be $313.84 - $312.73 ≈ $1.11