Question

consider the following scenarios: diana makes a single deposit of $700 into a savings account that pays a simple interest rate of 6.7%. denise makes a deposit of $700 every year into a savings account that pays a simple interest rate of 6.5%. leslie makes a single deposit of $700 into a savings account that pays an annual interest rate of 6.6% compounded monthly. bao makes a deposit of $700 every three months into a savings account that pays an annual interest rate of 6.5% compounded quarterly. who will have the most money in their savings account after 10 years, assuming no withdrawals were made?

Answer 1

Leslie, who makes a single deposit of $700 into a savings account with an annual interest rate of 6.6% compounded monthly, will have the most money in their savings account after 10 years, assuming no withdrawals were made.

Step-by-step explanation:

To determine who will have the most money after 10 years, we need to compare the future values of the savings accounts under different scenarios.

1. Diana's scenario:

`\[FV_D = P(1 + rt) = 700 * (1 + 0.067 * 10) = \$1,139.\]`

2. Denise's scenario:

`\[FV_{\text{Denise}} = P \left( ((1 + r)^t - 1)/(r) \right) = 700 * ((1 + 0.065)^(10) - 1)/(0.065) = \$8,974.\]`

3. Leslie's scenario (compounded monthly):

`\[FV_L = P \left(1 + (r)/(n)\right)^(nt) = 700 * \left(1 + (0.066)/(12)\right)^(12 * 10) = \$8,998.\]`

4. Bao's scenario (compounded quarterly):

`\[FV_B = P \left(1 + (r)/(n)\right)^(nt) = 700 * \left(1 + (0.065)/(4)\right)^(4 * 10) = \$8,896.\]`

After 10 years, Leslie will have the most money in their savings account, thanks to the compounding effect occurring monthly.

Answer 2

To determine who will have the most money in their savings account after 10 years, we calculate the future value for each scenario. Diana will have $1,539, Denise will have $9,758.66, and Leslie will have $1,547.58.

Step-by-step explanation:

To determine who will have the most money in their savings account after 10 years, we need to calculate the future value of each account using the given interest rates and compounding intervals.

For Diana, who made a single deposit of $700 with a simple interest rate of 6.7%, the formula to calculate the future value is: FV = P(1 + rt), where FV is the future value, P is the principal amount, r is the interest rate, and t is the time in years. Plugging in the values, we get FV = 700(1 + 0.067 * 10) = $1,539.

For Denise, who made a deposit of $700 every year with a simple interest rate of 6.5%, we can calculate the future value using the formula for the sum of an ordinary annuity: FV = PMT * [(1 + r)^t - 1] / r, where PMT is the annual deposit, r is the interest rate, and t is the time in years. Plugging in the values, we get FV = 700 * [(1 + 0.065)^10 - 1] / 0.065 = $9,758.66.

For Leslie, who made a single deposit of $700 at an annual interest rate of 6.6% compounded monthly, we can use the formula for compound interest: FV = P(1 + r/n)^(nt), where n is the number of compounding periods per year. Plugging in the values, we get FV = 700(1 + 0.066/12)^(12*10) = $1,547.58.