MATH SOLVE

5 months ago

Q:
# Sheldon invests $15,000 in an account earning 3% interest, compounded annually for 12 years. Seven years after Sheldon's initial investment, Howard invests $15,000 in an account earning 6% interest, compounded annually for 5 years. Given that no additional deposits are made, compare the balances of the two accounts after the interest period ends for each account. (round to the nearest dollar)

Accepted Solution

A:

Sheldon would have $21,386, while Howard would have $20,073.

The equation for each of these will be in the form

[tex]A=p(1+r)^t[/tex],

where A is the total amount in the account, p is the principal invested, r is the interest rate expressed as a decimal number, and t is the amount of time.

For Sheldon:

A=15000(1+0.03)¹²=15000(1.03)¹²=21386.41≈21386

For Howard:

A=15000(1+0.06)⁵=15000(1.06)⁵=20073.38≈20073

The equation for each of these will be in the form

[tex]A=p(1+r)^t[/tex],

where A is the total amount in the account, p is the principal invested, r is the interest rate expressed as a decimal number, and t is the amount of time.

For Sheldon:

A=15000(1+0.03)¹²=15000(1.03)¹²=21386.41≈21386

For Howard:

A=15000(1+0.06)⁵=15000(1.06)⁵=20073.38≈20073