Math Snap

STEP 1

Assumptions1. Anjana deposits $3000 in an account that earns simple interest at an annual rate of4.9%
. Darin deposits $3000 in an account that earns compound interest at an annual rate of4.9% and is compounded annually3. The time period for both investments is5 years

STEP 2

First, we need to calculate the amount in Anjana's account after5 years. For simple interest, the formula is$$A =(1 + rt)$$where- A is the amount of money accumulated after n years, including interest- is the principal amount (the initial amount of money)
- r is the annual interest rate (in decimal)
- t is the time the money is invested for, in years

STEP 3

Now, plug in the given values for, r, and t to calculate the amount in Anjana's account after5 years.
A = \($\)3000(1 +.9\% \times5)

STEP 4

Convert the percentage to a decimal value.
$$4.9\% =0.049$$A = \($\)3000(1 +0.049 \times)

STEP 5

Calculate the amount in Anjana's account after5 years.
A = \($\)3000(1 +0.049 \times5) = \($\)3675

STEP 6

Next, we need to calculate the amount in Darin's account after5 years. For compound interest, the formula is$$A =(1 + r/n)^{nt}$$where- A is the amount of money accumulated after n years, including interest- is the principal amount (the initial amount of money)
- r is the annual interest rate (in decimal)
- n is the number of times that interest is compounded per unit t- t is the time the money is invested for, in yearsSince the interest is compounded annually, n =1.

STEP 7

Now, plug in the given values for, r, n, and t to calculate the amount in Darin's account after5 years.
A = \($\)3000(1 +0.049/1)^{1 \times5}

Calculate the amount in Darin's account after5 years.
A = \($\)3000(1 +0.049)^5 = \($\)3728.24So, after5 years, Anjana will have $3675 in her account and Darin will have $3728.24 in his account.