Question

Suppose that Esther’s savings account earns an annual interest rate of 3.6% compounded monthly at the end of the month. Determine what just the first deposit of $50 will be worth at the end of a year, or 12 months. Use the interest rate and the formula for the future value of an investment.

Answer 1

Interest rate 0.3%

Future value $53.73

Explanation:

The interest rate per month is 3.6%12=0.3%.Esther's initial account balance is $50. To determine how much she'll have in 2 years, substitute the given values into the formula for the future value of an investment. Recall that the monthly interest rate is r/m

Answer 2

$51.83

Explanation:

Use the formula for amount after compound interest:
`FV = P(1 + i)^(n)`

"FV" is the future value, or total amount after the elapsed time

"P" is the principal, or starting investment

"i" is the interest rate each year

"n" is the number of compounding periods

Since interest is compounded monthly, the compounding time is 12.

Calculate "i" by dividing the (annual interest rate) by the (compounding time)

Convert the percentage to decimal form by dividing by 100.

i = 3.6% ÷ 12

= 0.036 ÷ 12

= 0.003

Calculate "n" by multiplying the (number of years) by the (compounding time)

n = 1*12 = 12

P = 50 because that is the deposit.

Substitute P, i and n into the equation

FV = P(1 + i)ⁿ

FV = 50(1 + 0.003)¹²

FV = 51.83

Therefore, the future value is $51.83.