Question

Jane wants to save money to buy a motorcycle. She invests in an ordinary annuity that earns 4.2% interest, compounded quarterly. Payments will be made at the end of each quarter. How much money will she need to pay into the annuity each quarter for the annuity to have a total value of $7000 after 3 years?

Answer 1

she need to pay is $550.40

Explanation:

given data

interest = 4.2 % compounded quarterly = 0.042 / 4 = 0.0105

future value = $7000

time = 3 year = 3 × 4 = 12 months

to find out

How much money she need to pay

solution

we will apply here formula for future value for compound quarterly

that is

future value = principal ×
`((1+r)^(t) -1 )/(r)` .............1

put here all these value

future value = principal ×
`((1+r)^(t) -1 )/(r)`

7000 = principal ×
`((1+0.0105)^(12) -1 )/(0.0105)`

principal = 550.40

so she need to pay is $550.40