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compute the future value in year 4 of a $500 deposit in year 1, and another $1,000 deposit at the end of year 3 using a 5 percent interest rate.

User KUTlime
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2 Answers

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Final answer:

To compute the future value in year 4 of a $500 deposit in year 1, and another $1,000 deposit at the end of year 3 using a 5 percent interest rate, the total future value is $1,150.

Step-by-step explanation:

To compute the future value in year 4 of a $500 deposit in year 1, and another $1,000 deposit at the end of year 3 using a 5 percent interest rate, we can use the simple interest formula. First, calculate the interest on the $500 deposit after 4 years:

Interest = Principal × rate × time
Interest = $500 × 0.05 × 4 = $100

Next, calculate the future value of the second deposit after 1 year:

Future value = Principal(1 + interest rate)time
Future value = $1,000(1 + 0.05)1 = $1,050

To find the total future value, add the interest earned from the first deposit to the future value of the second deposit:

Total future value = $100 + $1,050 = $1,150

User Xerillio
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3 votes

Final answer:

To calculate the future value of the deposits, we separately computed the future value of $500 over 4 years and $1,000 over 1 year using the formula Principal(1 + interest rate)^time, resulting in a total of $1,657.75 by the end of year 4.

Step-by-step explanation:

To compute the future value of two separate deposits using a 5 percent interest rate, we separate the calculations based on the timing of each deposit.

Calculating the Future Value for the First Deposit ($500)

For the $500 deposit made in year 1 and held until the end of year 4:

Future Value = Principal × (1 + interest rate)time

Future Value = $500 × (1 + 0.05)⁴

Future Value = $500 × (1.21550625)

Future Value = $607.75

Calculating the Future Value for the Second Deposit ($1000)

For the $1,000 deposit made at the end of year 3 and held until the end of year 4:

Future Value = Principal × (1 + interest rate)time

Future Value = $1,000 × (1 + 0.05)¹

Future Value = $1,000 × (1.05)

Future Value = $1,050

Combining Both Deposits

The total future value at the end of year 4 is:

Total Future Value = Future Value of First Deposit + Future Value of Second Deposit

Total Future Value = $607.75 + $1,050

Total Future Value = $1,657.75

User Elshnkhll
by
8.7k points

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