Question

Calculating Interest Rates. Solve for the unknown interest rate in each of the following.

PRESENT VALUE	YEARS	INTEREST RATE	FUTURE VALUE
$ 812	9		$ 2 491
1 120	6		2 829
19 500	21		252 942
66 500	18		423 925

Answer 1

Answer:

Situation 1:
Present Value = $812
Rate (r ) = ??
Time (n) = 9 years
Future Value = $2,491

Future Value = Present Value * (1 + r)^n
$2,491 = $812 * (1 + r)^ 9
$2,491 / $812 = (1 + r)^ 9
3.06773 = (1 + r)^ 9
3.06773 ^ (1/9) = 1 + r
1.1326 = 1 + r
r = 0.1326 or 13.26%

Interest Rate is 13.26%

Situation 2:
Present Value = $1,120
Rate (r ) = ??
Time (n) = 6 years
Future Value = $2,829

Future Value = Present Value * (1 + r)^n
$2,829 = $1,120 * (1 + r)^ 6
$2,829 / $1,120 = (1 + r)^ 6
2.52589 = (1 + r)^ 6
2.52589 ^ (1/6) = 1 + r
1.1670 = 1 + r
r = 0.1670 or 16.70%

Interest Rate is 16.70%

Situation 3:
Present Value = $19,500
Rate (r ) = ??
Time (n) = 21 years
Future Value = $252,942

Future Value = Present Value * (1 + r)^n
$252,942 = $19,500 * (1 + r)^ 21
$252,942 / $19,500 = (1 + r)^ 21
12.97138 = (1 + r)^ 21
12.97138 ^ (1/21) = 1 + r
1.1298 = 1 + r
r = 0.1298 or 12.98%

Interest Rate is 12.98%

Situation 4:
Present Value = $66,500
Rate (r ) = ??
Time (n) = 18 years
Future Value = $423,925

Future Value = Present Value * (1 + r)^n
$423,925 = $66,500 * (1 + r)^ 18
$423,925 / $66,500 = (1 + r)^ 18
6.37481 = (1 + r)^ 18
6.37481 ^ (1/18) = 1 + r
1.1084 = 1 + r
r = 0.1084 or 10.84%

Interest Rate is 10.84%