Question

Jamie deposits $1,600 into two different savings accounts. Account I is compounded annually at an interest rate of 2.75%. Account II is a simple interest investment with a 3 1/2% interest rate. What is the difference between the two accounts after 2 years?

Answer 1

Answer:

The correct answer is $22.79.

Step-by-step explanation:

Jamie deposits $1,600 into two different savings accounts.

Account I is compounded annually at an interest rate of 2.75%.

Time for the investment is 2 years.

Thus Amount in account I after two years time is

Principal × $(1 + \frac{interest rate}{100}) ^{time}$ = 1600 × $( 1 + \frac{2.75}{100} )^{2}$ = $1689.21.

Account II is a simple interest investment with a 3 1/2% = 3.5% interest rate.

Time for the investment is 2 years.

Thus Amount in account II after two years time is

Principal + Principal × time × $\frac{interest rate}{100}$= 1600 + 16 × 2 ×3.5 = 1600 + 112 = $1712

The difference between the two accounts after 2 years is

$ (1712 - 1689.21) = $22.79.

Answer 2

Answer:

Step-by-step explanation:

Considering account I, we would apply the formula for determining compound interest which is expressed as

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

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $1600

r = 2.75% = 2.75/100 = 0.0275

n = 1 because it was compounded once in a year.

t = 2 years

Therefore,

A = 1600(1 + 0.0275/12)^1 × 2

A = 1600(1.0275)^2

A = $1689.21

Considering account II, we would apply the formula for determining simple interest which is expressed as

I = PRT/100

Where

I represents interest paid on the investment.

P represents the principal or amount invested

R represents interest rate

T represents the duration of the investment in years.

From the information given,

P = 1600

R = 3.5

T = 2 years

I = (1600 × 3.5 × 2)/100 = $112

Total balance after 2 years is

112 + 1600 = $1712

the difference between the two accounts after 2 years is

1712 - 1689.21 = $22.79