The town of Escalon is issuing 10-year savings bonds so that they can build a new hospital. When the bonds mature the town will owe $3,250,000 to the bondholders. How much will the town need to deposit each quarter into a savings account with an APR of 2.25% in order to have enough to pay the bondholders upon maturity? Round your answer to 2 decimal places

$2,620,122.54

Step-by-step explanation:

Using the formula for calculating compound interest expressed as;

A = P(1+r/n)^nt

A is the amount = $3,250,000

P is the principal = x

t is the time = 10 years

r is the rate = 2.25% = 0.0225

n = (1/4)year (depositing each quarter)

Substituting the given values into the expression and get P as shown;

$3,250,000 = P(1+0.0225(4))^10(1/4)

$3,250,000 = P(1+0.09)^2.5

$3,250,000 = P(1.09)^2.5

$3,250,000 = P(1.2404)

P = $3,250,000/1.2404

P = $2,620,122.54

Hence the town need to deposit $2,620,122.54 each quarter into a savings account with an APR of 2.25% in order to have enough to pay the bondholders upon maturity

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step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

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etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

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