To solve Part A, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (in decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested for, in years
Given:
P = $200
r = 10% or 0.10
n = 1 (compounded annually)
t = 5 years
Plugging in the values, we get:
A = 200(1 + 0.10/1)^(1*5)
A = 200(1 + 0.10)^5
A = 200(1.10)^5
A ≈ 200(1.61051)
A ≈ $322.10
So, after 5 years, the value of Tristan's investment will be approximately $322.10.
For Part B, we'll use the same formula but with t = 10 years:
A = 200(1 + 0.10/1)^(1*10)
A = 200(1.10)^10
A ≈ 200(2.59374)
A ≈ $518.75
So, if Tristan leaves his money in the account for 10 years, the value of the investment will be approximately $518.75.
