Question

(Compound value solving for r​) At what annual rate would the following have to be​ invested?

a. $480 to grow to $1,350.08 in 1212 years

b. $300 to grow to ​$548.41 in 77 years

c. ​$52 to grow to ​$740.05 in 1919 years

d. ​$200 to grow to ​$252.50 in 44 years

Answer 1

This question requires application of basic time value of money function, according to which FV = PV * (1 + r)" where FV is Future Value, PV is present value, n is number of periods and r is rate per period

a) $1350.08 = $480 * (1 + r)¹²

2.8127 = (1 + r)¹²

1 + r = 1.09

r = 9.00%

b) $548.41 = $300 * (1 + r)⁷

1.8280 = (1 + r)⁷

1 + r = 1.09

r = 9.00%

c) $740.05 = $52 * (1 + r)¹⁹

14.2317 = (1 + r)¹⁹

1 + r = 1.15

r = 15.00%

d) $252.50 = $200 * (1 + r)⁴

1.2625 = (1 + r)⁴

1 + r = 1.06

r = 6.00%