Question

Find the best balance after investing $12,000 for a period of 7 years at two different interest earning types: simple interest at 5% and compound interest at 4.5%. Round the answer to two decimal places.

Answer 1

The balance after 7 years using simple interest at 5% is $16,200 and using compound interest at 4.5% is approximately $17,235.66. Compound interest yields a higher balance compared to simple interest for the same amount and period.

Step-by-step explanation:

The question involves calculating the balance of an investment after 7 years using two different interest earning methods: simple interest at a rate of 5% and compound interest at a rate of 4.5%.

Simple Interest Calculation:

Using the formula for simple interest

I = Prt,

where

I is the interest,

P is the principal amount ($12,000),

r is the rate of interest per year (0.05), and

t is the time in years (7),

we get:

I = $12,000 * 0.05 * 7 = $4,200

The total balance after 7 years with simple interest will be the principal plus the interest earned: $12,000 + $4,200 = $16,200.

Compound Interest Calculation:

Using the compound interest formula

A = P(1 + r/n)(nt),

where

A is the amount of money accumulated after n years, including interest,

P is the principal amount ($12,000),

r is the annual interest rate (0.045),

n is the number of times that interest is compounded per year, and

t is the time the money is invested for in years (7).

Assuming the interest is compounded once a year (n = 1), we get:

A = $12,000*(1 + 0.045/1)(1*7) = $12,000*(1.045)7 = $17,235.66 when rounded to two decimal places.

Comparing the two methods, the principle of compound interest results in a higher balance than simple interest over the same period, emphasizing its power to increase savings, especially over the long term.

Answer 2

The balance after 7 years using simple interest at 5% is $16,200 and using compound interest at 4.5% is approximately $17,235.66. Compound interest yields a higher balance compared to simple interest for the same amount and period.

Step-by-step explanation:

The question involves calculating the balance of an investment after 7 years using two different interest earning methods: simple interest at a rate of 5% and compound interest at a rate of 4.5%.

Simple Interest Calculation:

Using the formula for simple interest

I = Prt,

where

I is the interest,

P is the principal amount ($12,000),

r is the rate of interest per year (0.05), and

t is the time in years (7),

we get:

I = $12,000 * 0.05 * 7 = $4,200

The total balance after 7 years with simple interest will be the principal plus the interest earned: $12,000 + $4,200 = $16,200.

Compound Interest Calculation:

Using the compound interest formula

A = P(1 + r/n)(nt),

where

A is the amount of money accumulated after n years, including interest,

P is the principal amount ($12,000),

r is the annual interest rate (0.045),

n is the number of times that interest is compounded per year, and

t is the time the money is invested for in years (7).

Assuming the interest is compounded once a year (n = 1), we get:

A = $12,000*(1 + 0.045/1)(1*7) = $12,000*(1.045)7 = $17,235.66 when rounded to two decimal places.

Comparing the two methods, the principle of compound interest results in a higher balance than simple interest over the same period, emphasizing its power to increase savings, especially over the long term.

Answer 3

The best balance after investing $12,000 for 7 years at simple and compound interest rates of 5% and 4.5% respectively is $13,400 with simple interest and $14,226.79 with compound interest.

Step-by-step explanation:

To find the best balance after investing $12,000 for 7 years at two different interest earning types (simple interest at 5% and compound interest at 4.5%), we need to calculate the final amount for each type of interest.

For simple interest, the formula is Final Amount = Principal + (Principal * Rate * Time). Plugging in the values, we get Final Amount = $12,000 + ($12,000 * 0.05 * 7) = $13,400.

For compound interest, the formula is Final Amount = Principal * (1 + Rate/100)^Time. Plugging in the values, we get Final Amount = $12,000 * (1 + 0.045/100)^7 = $14,226.79.

Therefore, the best balance after investing $12,000 for 7 years is $14,226.79 when compounded annually at 4.5% interest.