Finding the interest rate and the number of years The future value and present v

Question

Finding the interest rate and the number of years The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations. If a security of $5,600 will be worth $9,869.11 five years in the future, assuming that no additional deposits or withdrawals are made, what is the implied interest rate the investor will earn on the security? 9.60% O 5.67% O 0.35% 12.00% If an investment of $50,000 is earning an interest rate of 12.00%, compounded annually, how long will it take for this investment to reach a value of $138,653.94, assuming that no additional deposits or withdrawals are made during this time? 9.00 years 0.31 years 2.77 years 3.61 years Which of the following are true, assuming that no additional deposits or withdrawals are made? It takes 10.50 years for $500 to double if invested at an annual rate of 5%. It takes 14.21 years for $500 to double if invested at an annual rate of 5%.

Explanation / Answer

1. FV = PV (1+r)n

$9869.11=$5600(1+r)5

(1+r)5 = 1.762341

By using Trial and error method or using future value of lumpsum table we can find 1.762341 value at 12% at 5 years.

r = 12%

2) FV = PV (1+r)n

$138,653.94 = $50,000(1.12)n

(1.12)n = 2.773079

By using Trial and error method or using future value of lumpsum table we can find 2.773079 value at 12% at 9 years

n= 9 years

3) It takes 14.21 years for $500 to double if invested at an annual rate of 5%.- True

FV = PV (1+r)n

= $500(1.05)14.21

= $500 *2.00032

= $1000.16

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