Question

Leslie deposits $1,600 into an account that earns 3.7% annual interest compounded quarterly. What will be

the total value of her investment after 4 years?

Answer 1

A = $1853.96

Explanation:

The formula for compound interest is

`A(t)=P(1+r/n)^n^t`, where A(t) is the amount, P is the principal (amount invested or deposited), r is the interest rate, n is the number of compound periods per year, and t is the time in years.

• For the problem, our P value is $1600
• Our r value is 0.037 (we must convert the percent to a decimal)
• Our n value is 4 (quarterly means 4 so the money is compounded once every 3 months since there 3 months make up a quarter in a year)
• Our t value is 4
• We must solve for A(t)

`A(t)=1600(1+0.037/4)^(^4^*^4^)\\A(t)=1600(1.00925)^1^6\\A(t)=1853.958942\\A(t)=1853.96`