Question

Prairie grains cooperative wants to invest $48,000 in a short-term deposit. The bank offers 1.2% interest for a one-year term and 1.1% for a six-month term. (a) How much would Prairie grains receive if the $48,000 is invested for one year? (b) How much would Prairie grains receive at the end of one year if the $48,000 is invested for six months and then the principal and interest earned is reinvested for another six months? (c) What would the one-year rate have to be to yield the same amount of interest as the investment described in part (b)?

Answer 1

(a) Prairie Grains would receive $48,576 if the $48,000 is invested for one year at a 1.2% interest rate.

(b) If Prairie Grains invests $48,000 for six months at a 1.1% interest rate, it would receive $24,444 at the end of the first six months. Reinvesting this amount for the remaining six months at the same 1.1% rate, the total amount at the end of the year would be approximately $48,816.

(c) To yield the same amount of interest as in part (b), the one-year rate would need to be approximately 1.7%.

Step-by-step explanation:

(a) For part (a), the interest is calculated using the formula A = P(1 + r), where A is the amount after interest, P is the principal amount, and r is the interest rate. Plugging in the values, we get A = $48,000 * (1 + 0.012) = $48,576.

(b) In part (b), the interest for the first six months is calculated as $48,000 * 0.011 = $528. Adding this to the principal gives $48,528, which is then reinvested for the next six months at the same rate, resulting in a final amount of approximately $48,816.

(c) To find the one-year rate that would yield the same interest as in part (b), we use the formula A = P(1 + r/2
`)^2`, where r is the interest rate for six months. Solving for r, we find that it needs to be approximately 0.017 or 1.7% for the one-year rate to match the interest earned in part (b).