Question

Modeling real life you want to save money for a trip to the cocoa beach pier. you deposit $920 in an account that earns simple interest at an annual rate of 10%. travel and entertainment will cost $600, and lodging will cost $800. a. how many years will it take for you to save enough money for the trip

Answer 1

To calculate the number of years it will take for you to save enough money for the trip, we need to consider the amount of money you have already saved, the annual interest rate, and the expenses involved in the trip. Let's break it down: Starting with $920 in your account and assuming you don't withdraw any money from it, each year, the account will earn 10% interest on the total balance. The total cost of the trip is $600 (travel and entertainment) + $800 (lodging), which is $1,400 in total. You want to save enough money to cover the cost of the trip. So, let's calculate how many years it will take for your savings to reach or exceed $1,400: Year 1: $920 + $92 (10% of $920) = $1,012 Year 2: $1,012 + $101.2 (10% of $1,012) = $1,113.2 Year 3: $1,113.2 + $111.32 (10% of $1,113.2) = $1,224.52 Continuing this pattern, we can calculate the balance at the end of each year until it exceeds $1,400. The number of years it takes is the total number of years it will take for your savings to reach or exceed $1,400, which in this case is 5 years.

Step-by-step explanation:

To calculate the number of years it will take for you to save enough money for the trip, we need to consider the amount of money you have already saved, the annual interest rate, and the expenses involved in the trip.

Let's break it down:

1. Starting with $920 in your account and assuming you don't withdraw any money from it,
2. Each year, the account will earn 10% interest on the total balance.
3. The total cost of the trip is $600 (travel and entertainment) + $800 (lodging), which is $1,400 in total.
4. You want to save enough money to cover the cost of the trip. So, let's calculate how many years it will take for your savings to reach or exceed $1,400:

Year 1: $920 + $92 (10% of $920) = $1,012
Year 2: $1,012 + $101.2 (10% of $1,012) = $1,113.2
Year 3: $1,113.2 + $111.32 (10% of $1,113.2) = $1,224.52

Continuing this pattern, we can calculate the balance at the end of each year until it exceeds $1,400. The number of years it takes is the total number of years it will take for your savings to reach or exceed $1,400, which in this case is 5 years.