Question

(Compound value solving for r) At what annual rate would the following have to be invested? a. $480 to grow to $1,238.60 in 11 years b. $300 to grow to $450.22 in 6 years c. $52 to grow to $516.55 in 22 years d. $220 to grow to $280.78 in 5 years a. At what annual rate would $480 have to be invested to grow to $1,238.60 in 11 years? % (Round to the nearest whole percent.)

Answer 1

Answer to Part a.

Present Value = $480.00
Future Value = $1,238.60
Rate (r ) = ??
Time = 11 years

Future Value = Present Value * (1 + r)^ n
$1,238.60 = $480.00 * (1 + r)^ 11
2.5804 = (1 + r)^ 11
(2.5804)^ (1/11) = 1 + r
1.0900 = 1 + r
r = 0.0900
r = 9%

Answer to Part b.

Present Value = $300.00
Future Value = $450.22
Rate (r ) = ??
Time = 6 years

Future Value = Present Value * (1 + r)^ n
$450.22 = $300.00 * (1 + r)^ 6
1.5007 = (1 + r)^ 6
(1.5007)^ (1/6) = 1 + r
1.0700 = 1 + r
r = 0.0700
r = 7%

Answer to Part c.

Present Value = $52
Future Value = $516.55
Rate (r ) = ??
Time = 22 years

Future Value = Present Value * (1 + r)^ n
$516.55 = $52.00 * (1 + r)^ 22
9.9337 = (1 + r)^ 22
(9.9337)^ (1/22) = 1 + r
1.1100 = 1 + r
r = 0.1100
r = 11%

Answer to Part d.

Present Value = $220.00
Future Value = $280.78
Rate (r ) = ??
Time = 5 years

Future Value = Present Value * (1 + r)^ n
$280.78 = $220.00 * (1 + r)^ 5
1.2763 = (1 + r)^ 5
(1.2763)^ (1/5) = 1 + r
1.0500 = 1 + r
r = 0.0500
r = 5%