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QuestionSouthern Land Company needs to raise \$300,000 in 3 years with quarterly payments at 8\% interest. Find the quarterly payment.

Studdy Solution

STEP 1

Assumptions1. The target amount is $300,000. The interest rate is8% per year3. The time for investment is3 years4. The interest is compounded quarterly5. The company plans to make equal quarterly investments

STEP 2

First, we need to find the number of quarters in years. There are4 quarters in a year, so we can calculate this by multiplying the number of years by4.
Number of quarters=Yearstimes4Number\, of\, quarters = Years \\times4

STEP 3

Now, plug in the given value for the number of years to calculate the number of quarters.
Number of quarters=3timesNumber\, of\, quarters =3 \\times

STEP 4

Calculate the number of quarters.
Number of quarters=3times4=12Number\, of\, quarters =3 \\times4 =12

STEP 5

Next, we need to find the quarterly interest rate. We can do this by dividing the annual interest rate by the number of quarters in a year.
Quarterly interest rate=Annual interest rate/4Quarterly\, interest\, rate = Annual\, interest\, rate /4

STEP 6

Now, plug in the given value for the annual interest rate to calculate the quarterly interest rate.
Quarterly interest rate=8%/4Quarterly\, interest\, rate =8\% /4

STEP 7

Convert the percentage to a decimal value.
%=0.08\% =0.08Quarterly interest rate=0.08/4Quarterly\, interest\, rate =0.08 /4

STEP 8

Calculate the quarterly interest rate.
Quarterly interest rate=0.08/4=0.02Quarterly\, interest\, rate =0.08 /4 =0.02

STEP 9

Now, we can use the formula for the sinking fund to calculate the quarterly payment. The formula isPayment=Target amount/((+Quarterly interest rate)Number of quarters−)/Quarterly interest ratePayment = Target\, amount / (( + Quarterly\, interest\, rate)^{Number\, of\, quarters} -) / Quarterly\, interest\, rate

STEP 10

Plug in the values for the target amount, the quarterly interest rate, and the number of quarters to calculate the payment.
Payment=$300,000/((+0.02)12−)/0.02Payment = \$300,000 / (( +0.02)^{12} -) /0.02

STEP 11

Calculate the payment.
Payment=$300,000/((+0.02)−)/0.02=$21,690.26Payment = \$300,000 / (( +0.02)^{} -) /0.02 = \$21,690.26The company needs to make quarterly payments of $21,690.26.

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