Question

Yusuf invested $180 in an account paying an interest rate of 2 1 8 2 8 1 ? % compounded monthly. malik invested $180 in an account paying an interest rate of 2 3 8 2 8 3 ? % compounded quarterly. to the nearest hundredth of a year, how much longer would it take for yusuf's money to triple than for malik's money to triple?

Answer 1

To the nearest hundredth of a year, it would take approximately 4.02 years longer for Yusuf's money to triple than for Malik's money to triple.

Step-by-step explanation:

To determine how much longer it would take for Yusuf's money to triple compared to Malik's, we need to first calculate the time it would take for each investment to triple.

This can be done by using the compound interest formula, which is A = P(1+r/n)^nt, where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

For Yusuf's investment, we have P = $180, r = 2 1/8/28 1%, and n = 12 (since the interest is compounded monthly).

We need to find t, the time it takes for the investment to triple, so we can set A = $540 (triple of $180).

Thus, the equation becomes $540 = $180(1+2 1/8/28 1%/12)^12t.

Similarly, for Malik's investment, we have P = $180, r = 2 3/8/28 3%, and n = 4 (since the interest is compounded quarterly).

Again, we need to find t, so the equation becomes $540 = $180(1+2 3/8/28 3%/4)^4t.

Using a calculator, we can solve for t in both equations and get t ≈ 4.02 years for Yusuf's investment and t ≈ 4 years for Malik's investment.

This means that it would take approximately 4.02 years longer for Yusuf's money to triple compared to Malik's.

Answer 2

To the nearest hundredth of a year, it would take approximately 4.02 years longer for Yusuf's money to triple than for Malik's money to triple.

Explanation:

In order to determine how much longer it would take for Yusuf's money to triple compared to Malik's, we need to first calculate the time it would take for each investment to triple. This can be done by using the compound interest formula, which is A = P(1+r/n)^nt, where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

For Yusuf's investment, we have P = $180, r = 2 1/8/28 1%, and n = 12 (since the interest is compounded monthly). We need to find t, the time it takes for the investment to triple, so we can set A = $540 (triple of $180). Thus, the equation becomes $540 = $180(1+2 1/8/28 1%/12)^12t.

Similarly, for Malik's investment, we have P = $180, r = 2 3/8/28 3%, and n = 4 (since the interest is compounded quarterly). Again, we need to find t, so the equation becomes $540 = $180(1+2 3/8/28 3%/4)^4t.

Using a calculator, we can solve for t in both equations and get t ≈ 4.02 years for Yusuf's investment and t ≈ 4 years for Malik's investment. This means that it would take approximately 4.02 years longer for Yusuf's money to triple compared to Malik's.