Final answer:
To find out how much the savings account will be worth in 49 months, we can use the formula for compound interest. Plugging in the given values, the account will be worth approximately $16082.32 after 49 months.
Step-by-step explanation:
To find out how much the savings account will be worth in 49 months, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount in the account after t years
- P is the principal (initial amount) of the account
- r is the annual interest rate (as a decimal)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, the principal (P) is $9100, the annual interest rate (r) is 14.86% or 0.1486, the number of times interest is compounded per year (n) is 2 (semi-annually), and the number of years (t) is 49 months, which is approximately 4.083 years. Plugging in these values into the formula, we get:
A = $9100(1 + 0.1486/2)^(2*4.083)
Calculating this expression, the account will be worth approximately $16082.32 after 49 months.