Larry invested $27,000 in a savings account that pays an annual interest rate of 1.8%. The savings account is set to compound quarterly . How much is in Larry’s account after 5 years?
What is the initial value?
What is the rate?
How many times a year is the money compounded?
How much is in his account after five year?
To find the initial value, we know that Larry invested $27,000 in the savings account. So the initial value is $27,000.
The rate of interest is 1.8% or 0.018 as a decimal.
The money is compounded quarterly, which means it is compounded 4 times a year.
To find the amount in Larry's account after 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment
P = the principal amount (initial value)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
Plugging in the values:
A = 27000 * (1 + 0.018/4)^(4*5)
A = 27000 * (1.0045)^(20)
A ≈ 27000 * 1.09416206
A ≈ $29,535.97
So there is approximately $29,535.97 in Larry's account after 5 years.