MATH SOLVE

2 months ago

Q:
# Tyler has earned money by helping out on a neighbor's farm and now wants to put his earnings in a savings account. He is a bit confused on the different interest options available and how each will impact the amount he has after several years. Help Tyler better understand by showing him how his money will increase in an account that uses simple interest and one that uses compound interest over a specified period of time. 1. a. If Tyler deposits $1500 of the $3200 he has earned in an account that pays 4% interest compounded annually, how much will he have in his account after 5 years?2. B. If Tyler deposits $1500 of the $3200 he has earned in an account that pays 4% simple interest, how much will he have after 5 years? Show all work.3. c. Which account would yield a greater amount? What is the difference between the two amounts?

Accepted Solution

A:

1. The applicable interest formula is

I = Prt

where P is the principal amount invested, r is the interest rate (% per year), and t is the time in years.

Substituting the given information, the interest is computed to be

I = 1500×0.04×5 = 300

This amount of interest is added to Tyler's account, so at the end of 5 years, he will have

$1500 +300 = $1,800.00

2. The formula applicable to the account balance (A) is

A = P(1+r)^t

where P, r, and t are defined as above.

Substituting the given numbers, we find the balance at the end of 5 years to be

A = 1500(1+.04)^5 ≈ $1,824.98

3. The account earning compound interest yields the greater amount by

$1,824.98 - $1,800.00 = $24.98

I = Prt

where P is the principal amount invested, r is the interest rate (% per year), and t is the time in years.

Substituting the given information, the interest is computed to be

I = 1500×0.04×5 = 300

This amount of interest is added to Tyler's account, so at the end of 5 years, he will have

$1500 +300 = $1,800.00

2. The formula applicable to the account balance (A) is

A = P(1+r)^t

where P, r, and t are defined as above.

Substituting the given numbers, we find the balance at the end of 5 years to be

A = 1500(1+.04)^5 ≈ $1,824.98

3. The account earning compound interest yields the greater amount by

$1,824.98 - $1,800.00 = $24.98