You account pays interest at 8 percent p.a. You deposit $35,945 in it today. You must have exactly $88,956 in the account at the end of two years. What should you do at the end of the first year to ensure this?
Answer: $43,544.99
Can anyone show me the steps to solve this problem? Thanks!
To solve this problem, we need to calculate the interest earned after one year and then determine how much additional money needs to be deposited to reach the desired amount at the end of two years.
Step 1: Calculate the interest earned after one year.
The formula to calculate simple interest is:
Interest = Principal * Rate * Time
Given:
Principal (P) = $35,945
Rate (R) = 8% per annum or 0.08
Time (T) = 1 year
Interest = $35,945 * 0.08 * 1
Interest = $2,875.60
Step 2: Determine the additional amount to be deposited at the end of the first year.
We want the total amount in the account to reach $88,956 at the end of two years. Since we have already earned $2,875.60 in interest after one year, we need to deposit an additional amount that, with the interest earned after the second year, will bring the total to $88,956.
Additional amount = Desired final amount - (Principal + Interest earned after one year)
Additional amount = $88,956 - ($35,945 + $2,875.60)
Additional amount = $88,956 - $38,820.60
Additional amount = $50,135.40
Therefore, you should deposit an additional amount of $50,135.40 at the end of the first year to ensure that you have exactly $88,956 in the account at the end of two years.