Question

2) Marion deposited $12,000 into her saving account for 10 years with simple annual interest rate of 5%. Cameron deposited $12,000 into his saving account with annual compound interest rate of 4% for 10 years. Which account will have more money after 10 years and by how much.

Answer 1

Answer:

Marion’s account will have $237 more at the end of 10 years

Step-by-step explanation:

Firstly, we calculate the amount that will be in Marion’s account after 10 years.

To calculate this, we use the formula for simple interest

I = PRT/100

where I is the interest accrued for the period of years

P is the amount deposited = $12,000

R is the rate = 5%

T is the time which is 10 years

Plugging these values into the equation

I = (12,000 * 5 * 10)/100 = $6,000

The amount after 10 years is thus the sum of the amount deposited and the interest accured = $12,000 + $6,000 = $18,000

Now for Cameron, we use the compound interest formula

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

Where A is the amount in the account after the number of years

P is the amount deposited = $12,000

r is the interest rate = 4% = 4/100 = 0.04

n is the number of times per year the interest is compounded. Since it is annually, n = 1

t is the time which is 10 years

We plug these values and we have;

A = 12,000(1 + 0.04/1)^(1 * 10)

A = 12,000 (1.04)^10

A = $17,763 ( to the nearest whole dollars)

Since 18,000 is greater than 17,763, the amount in Marion’s account will be greater at an amount of (18,000 - 17,763) = $237