Question

What is the interest rate if a deposit subject to annual compounding is doubled after 5 years?

Answer 1

Answer)

Calculation of annual compounding rate of interest

Maturity value = Investment amount X Future value of $ 1 at required rate for 5 years

Future value of $ 1 at required rate for 5 years= Maturity value/ Investment amount

                                                                                    = $ 2.00/ $ 1.00

                                                                                    = 2.00000

On a perusal of future value of $ 1 table at 5 years, figures corresponding to 14% is 1.925415 and 15% is 2.011357.

It implies that interest rate of deposit should be between 14% and 15%. On extrapolating between these we get:

                           = 14% + (2.00000- 1.925415)/ (2.011357 – 1.925415)

                           = 14% + (0.074585/ 0.085942)

                           = 14.8678% of 14.868% (approximately)

Therefore at annual compounding rate of 14.868%, $1 invested will double in 5 years.