Question

Find the value of the ordinary annuity at the end of the indicated time period. The payment​ R, frequency of deposits m​ (which is the same as the frequency of​ compounding), annual interest rate​ r, and time period t are given.

Amount$1,000; quarterly; 6.1%; 6 years

The value of the ordinary annuity is $___

Answer 1

Future Value of an Ordinary Annuity

Here, we’ve quarterly deposit (P) = $1,000

Quarterly interest rate (r) = 1.525% [6.10% / 4 Quarters]

Number of periods (n) = 24 Years [6 Years x 4 Quarters]

Therefore, Future Value of an Ordinary Annuity = P x [{(1+ r)ⁿ - 1} / r ]

= $1,000 x [{(1 + 0.01525)²⁴ - 1} / 0.01525]

= $1,000 x [(1.437977054 – 1) / 0.01525]

= $1,000 x [0.437977054 / 0.01525]

= $1,000 x 28.71980679

= $28,719.81

Hence, the value of the ordinary annuity is $28,719.81