Question

Find the future value at the end of 7 years of $1300 invested today at an interest rate of 10 per cent compounded semiannually.

Answer 1

Future value is the sum total of interest earned in all invested years and the initial amount invested.

Future value is calculated below

Schedule of Future Value
Year	Beginning Balance	Interest earned during year	Ending balance
1	$ 1,300.00	$ 130.00	$ 1,430.00
2	$ 1,430.00	$ 143.00	$ 1,573.00
3	$ 1,573.00	$ 157.30	$ 1,730.30
4	$ 1,730.30	$ 173.03	$ 1,903.33
5	$ 1,903.33	$ 190.33	$ 2,093.66
6	$ 2,093.66	$ 209.37	$ 2,303.03
7	$ 2,303.03	$ 230.30	$ 2,533.33
Future value			$ 2,533.33

First year’s interest is calculated on $1300 and interest earned in first year is $130. In second year interest is earned on ($1300+130) $1430 which is principle amount plus interest earned in year 1. Similarly interest income increases the value of investment every year and interest is calculated on updated investment value.

Future value of $1300 invested fo0r 7 Years at 10% Interest is $ 2533.33

or $2533 approx.