Question

Show how to solve this problem with formula:

a) Johanna wants to start saving for a vacation and plans to save monthly for four years. She plans to deposit $120 each month into an account earning 9 percent, compounded monthly. How much will she have in her account in four years?

b) How much will she have if she starts saving immediately and makes deposits at the beginning of each month?

Answer 1

a)

Rate = 9% / 12 = 0.75%

Number of periods = 4 * 12 = 48

Future value = Annuity * [(1 + r)ⁿ - 1] / r

Future value = 120 * [(1 + 0.0075)⁴⁸ - 1] / 0.0075

Future value = 120 * 57.520711

Future value = $6,902.49

b)

Rate = 9% / 12 = 0.75%

Number of periods = 4 * 12 = 48

Future value of annuity due = (1 + r) * Annuity * [(1 + r)ⁿ - 1] / r

Future value annuity due = (1 + 0.0075) * 120 * [(1 + 0.0075)⁴⁸ - 1] / 0.0075

Future value annuity due = (1.0075) * 120 * 57.520711

Future value annuity due = $6,954.25