Compound Interest Doubling Time Formula

Compound Interest Doubling Time Formula

This following formula is used to calculate the period in which the amount would be doubled using the prevailing interested rate.

Doubling period Formula = ln(2)/r

r= interest Rate

Example

Interest rate =9%

Doubling Period?

Solution

Doubling Period Formula = ln(2)/r

=ln (2)/9%

=ln(2)/.09

=7.70 Years

It takes 7.7 years that an amount would be doubled. for example if 10,000 was invested ,then it would be 20,000 in 7.7 years.

Future Value of Growing Annuity Formula

Future Value of Growing Annuity Formula

There may be a growing series of payment deposited with institution to receive lump sum amount on maturity. Series of payment grow at gradual rate. The future value of such annuity may be calculated by following formula

Annuity Factor =Cx [(1+i)ⁿ-(1+g)ⁿ]

                                  i-g

i= interest Rate

g=Growth rate

n= period

C=Deposited amount

Example

Deposit = 10,000

Growth Rate of deposit = 5%

Interest Rate = 9%

Period =10 Years

Solution

Annuity Factor =10,000x [(1+9%)¹⁰-(1+5%)¹⁰]

                                            9%-5%

=10000 x [2.367 – 1.6288]/.09-.05

=184,550

Future Value of Annuity Due Formula

Future Value of Annuity Due Formula

Future value of annuity is calculated to determine the future value of the series of payment. This concept is widely used in insurance company.

Annuity Factor =Cx [(1+i)ⁿ-1] x (1+r)

                              i

Example

Amount Deposited= 2000

Period = 5 Years

Interest Rate =9%

Solution

Annuity Factor =C x [(1+i)ⁿ-1] x (1+r)

                               i

= Cx [(1+9%)⁵-1] x (1+9%)

           9%

=5.984 x 1.09

=6.5233

=6.5233 X 2000

=13,047

MIRR Formula

MIRR Formula

IRR use the same rate for reinvestment of fund, which is not practical. Therefore MIRR concept has been introduced, which uses the cost of capital as reinvestment.

MIRR = n√A/B

n= life of project

A= Recovery phase Cash flows

B= Investment phase Cash flow

Example

Year               Cash Flows

0                          (100,000)

1                            (20,000)

2                             50,000

3                             50,000

4                             40,000

5                            (20,000)

IRR is 12% and discount Rate is 8%, Calculate MIRR?

Solution

Investment Phase discounting

Year       Cash Flows      Discount              PV

0               (100,000)          1                      (100,000)

1                (20,000)          (1.08)^-1                   (18,518)

Total                                                           118,518

Recovery Phase flows

Year     Cash Flows       Discount         PV

2                  50,000          (1.08)³           62986

3                  50,000          (1.08)²           58320

4                  40,000           (1.08)¹          43200

5                  (20,000)          1                (20000)

                                                               144,506

MIRR = n√A/B -1

= 5√144,506/118518

=4.04%