Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added itself also earns interest. Suppose you open an account that pays a guaranteed fixed interest rate of 5%, compounded annually (every year). You make no further contributions; you just leave your money alone and let compound interest work its magic. Suppose that you deposit $1000.00 (starting principal) into the account when you open it. In the second year, you have in your account: 1000.00 + 1000.00 × 5% = 1050.00 In the third year, you have 1050.00 + 1050.00 × 5%in your account, and so on. It is easy to see that if an represents the balance of your account in n-th year, we have the following relation:an =an−1+an−1×0.05=1.05×an−1. Given the recursive relation and the initial condition of a1 = 1000.0, find out the closed formular for an, and calculates the account balance in the 10th year.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
-
Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added itself also earns interest. Suppose you open an account that pays a guaranteed fixed interest rate of 5%, compounded annually (every year). You make no further contributions; you just leave your money alone and let compound interest work its magic. Suppose that you deposit $1000.00 (starting principal) into the account when you open it. In the second year, you have in your account:
1000.00 + 1000.00 × 5% = 1050.00 In the third year, you have
1050.00 + 1050.00 × 5%
in your account, and so on. It is easy to see that if an represents the balance of youraccount in n-th year, we have the following relation:
an =an−1+an−1×0.05=1.05×an−1.Given the recursive relation and the initial condition of a1 = 1000.0, find out the closed formular for an, and calculates the account balance in the 10th year.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
