Question

Which formula do i use for this? it seems i used the wrong one.

Answer 1

The total amount of money which the Stewart family would have to pay into the annuity each quarter is $242.12.

How to calculate the payment?

Mathematically, annuity can be calculated by using this formula:

$A = P[\frac{(1+\frac{r}{n} )^{nt} - 1)}{\frac{r}{n} }]$

Given the following data:

• Time, t = 11 years.

• Number of times compounded (quarterly), n = 4.

• Present value, A = $13,000.

• Interest rate, r = 3.6% = 0.036.

Substituting the given parameters into the formula, we have;

$13000 = P[\frac{(1+\frac{0.036}{4} )^{4 \times 11} - 1)}{\frac{0.036}{4} }]\\\\13000 = P[\frac{(1+0.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{(1.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{1.48323960867 - 1}{0.009 }]\\\\13000 = P[\frac{0.48323960867 }{0.009 }]\\\\13000 = 53.6932898522P$

P = 13000/53.6932898522

P = $242.12.

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Complete Question:

The Stewart family wants to save money to travel the world. They plan to invest in an ordinary annuity that earns 3.6% interest, compounded quarterly. Payments will be made at the end of each quarter. How much money do they need to pay into the annuity each quarter for the annuity to have a total value of $13,000 after 11 years?