Question

When they are first​ born, Grandma gives each of her grandchildren a ​$5,000 savings bond that matures in 18 years. For each of the following​ grandchildren, what is the present value of each savings bonds if the current discount rate is 4.5​%? a.  Seth turned fourteen years old today. b. Shawn turned twelve years old today. c.  Sherry turned nine years old today. d. Sheila turned five years old today. e. Shane was just born.

Answer 1

Answer to Part a.

Future Value = $5,000
Rate (r) = 4.50%
Time (n) = 4 years
Present Value (PV) = ??

Future Value = Present Value * (1 + r)^ n
$5,000 = Present Value * (1 + 0.045) ^4
$5,000 = Present Value * 1.045^4
$5,000 = Present Value * 1.1925
Present Value = $4,192.87

Answer to Part b.

Future Value = $5,000
Rate (r) = 4.50%
Time (n) = 6 years
Present Value (PV) = ??

Future Value = Present Value * (1 + r)^ n
$5,000 = Present Value * (1 + 0.045) ^6
$5,000 = Present Value * 1.045^6
$5,000 = Present Value * 1.3023
Present Value = $3,839.36

Answer to Part c.

Future Value = $5,000
Rate (r) = 4.50%
Time (n) = 9 years
Present Value (PV) = ??

Future Value = Present Value * (1 + r)^ n
$5,000 = Present Value * (1 + 0.045) ^9
$5,000 = Present Value * 1.045^9
$5,000 = Present Value * 1.4861
Present Value = $3,364.51

Answer to Part d.

Future Value = $5,000
Rate (r) = 4.50%
Time (n) = 13 years
Present Value (PV) = ??

Future Value = Present Value * (1 + r)^ n
$5,000 = Present Value * (1 + 0.045) ^13
$5,000 = Present Value * 1.045^13
$5,000 = Present Value * 1.7722
Present Value = $2,821.35

Answer to Part e.

Future Value = $5,000
Rate (r) = 4.50%
Time (n) = 18 years
Present Value (PV) = ??

Future Value = Present Value * (1 + r)^ n
$5,000 = Present Value * (1 + 0.045) ^18
$5,000 = Present Value * 1.045^18
$5,000 = Present Value * 2.2085
Present Value = $2,263.98