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You plan to accumulate $24,000 for a car in 5 years’ time. To do this, you...

You plan to accumulate $24,000 for a car in 5 years’ time. To do this, you will make 20 level deposits (quarterly) with the first deposit today. If you earn 14.7% per annum compounding quarterly, what regular deposit will be needed? (round to nearest cent; don’t use $ sign or commas)

a. $803.97

b. $833.52

c. $1708.55

d. $3121.87

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Answer #1

The amount to be deposited at the beginning of each quarter

Here, we’ve Future Value = $24,000

Quarterly interest rate (r) = 3.675% per quarter [14.70% / 4 Quarters]

Number of periods (n) = 20 Periods [5 Years x 4 Quarters]

Amount to be deposited at the beginning of each quarter (P) = ?

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

$24,000 = (1 + 0.03675) x P x [{(1 + 0.03675)20 - 1} / 0.03675]

$24,000 = 1.03675 x P x [(2.05816828 – 1) / 0.03675]

$24,000 = 1.03675 x P x [1.05816828 / 0.03675]

$24,000 = 1.03675 x P x 28.7936947

$24,000 = P x 29.85186298

Therefore, P = $24,000 / 29.85186298

P = $803.97

“Hence, the amount to be deposited at the beginning of each quarter will be $803.97”

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