Question

Arianys invested $61,000 in an account paying an interest rate of 7 1/8%compounded continuously. Yusuf invested $61,000 in an account paying an interest rate of 7 5/8% compounded monthly. After 14 years, how much more money would Yusuf have in his account than Arianys, to the nearest dollar?

Answer 1

after 14 years, Yusuf would have approximately $9,645.57 more in his account than Arianys (rounded to the nearest dollar).

Explanation:

Certainly! Let's calculate the future values for Arianys and Yusuf and find the difference between them after 14 years.

For Arianys:

Principal amount (P) = $61,000

Interest rate (r) = 7 1/8% = 7.125% = 0.07125 (in decimal form)

Time (t) = 14 years

Using the formula for continuous compounding:

A_arianys = P * e^(rt)

A_arianys = $61,000 * e^(0.07125 * 14)

Using a calculator, we find that A_arianys is approximately $151,564.27 (rounded to the nearest cent).

For Yusuf:

Principal amount (P) = $61,000

Interest rate (r) = 7 5/8% = 7.625% = 0.07625 (in decimal form)

Time (t) = 14 years

Compounding periods per year (n) = 12 (monthly compounding)

Using the formula for compound interest:

A_yusuf = P * (1 + r/n)^(nt)

A_yusuf = $61,000 * (1 + 0.07625/12)^(12 * 14)

Using a calculator, we find that A_yusuf is approximately $161,209.84 (rounded to the nearest cent).

Now, let's find the difference between A_yusuf and A_arianys:

Difference = A_yusuf - A_arianys

Difference = $161,209.84 - $151,564.27

Difference = $9,645.57 (rounded to the nearest cent)

Therefore, after 14 years, Yusuf would have approximately $9,645.57 more in his account than Arianys (rounded to the nearest dollar).