Question

Your grandmother invested $2,300 for you on the day you were born. This investment has earned an average of 13.8 percent annually. How old are you if the investment is now worth $18,642? O 14.36 years 14.58 years 15.15 years 16.19 years

Answer 1

1.

Grandmother Invested = $ 2,300

Current Value of Investment = $ 18,642

Interest Rate = 13.8 % annually

If Interest compounded annually, then -

Future Value of Initial Investment = Initial Investment(1 + i )^t

Where,

i = Interest rate

t = Time (years)

In above case, Initial Investment = $ 2,300

Future Value of Initial Investment in t(time) = $ 18,642

Now, Computation of Time(t)

2,300(1 + 0.138)^t = 18,642

(1.138)^t = 18,642/2,300

(1.138)^t = 8.1052

Applying Log both side,

t*Log(1.138) = Log(8.1052)

t = Log(8.1052) / Log (1.138)

t = 0.9088 / 0.0561

t = 16.19 years

It takes 16.19 years at 13.8 % annually to make initial investment $ 2,300, worth $ 18,642

2.

Initial Investment = $ 7,100

Future value of Investment = $ 12,000

Interest rate = 7.25 % or 0.0725

Time = t

Computation of Time(t)

7,100(1 + 0.0725)^t = 12,000

(1.0725)^t = 12,000/7,100

(1.0725)^t = 1.690

Applying Log both side,

t*Log(1.0725) = Log(1.690)

t = Log(1.690) / Log (1.0725)

t = 0.2279 / 0.0304

t = 7.50 years

It takes 7.50 years at 7.25 % annually to make initial investment $ 7,100, worth $ 12,000

3.

Simple Interest method refers where interest is fixed for each period and Compound Interest method refers where Interest calculated on compound value (Principal + Previous Interest) for each period.

Simple Interest Method

A = P + P*R*T

Where,

A = Amount (Future Value)

P = Principal (Initial Investment)

R = Interest Rate

T = Time

Compound Interest Method

A = P(1+R)^T

Where,

A = Amount (Future Value)

P = Principal (Initial Investment)

R = Interest Rate

T = Time

In above case, $ 73,000 in deposited in each Bank

First city Bank pays 7% simple interest for 9 years

Therefore, Deposit value after 9 years would be

A = P + P*R*T

A = 73,000 + 73,000*0.07*9

A = 73,000 + 45,990

A = 118,990

Deposit value after 9 years would be $ 118,990 in First City Bank.

Second city Bank pays 7% Compound interest for 9 years

Therefore, Deposit value after 9 years would be

A = P(1+R)^T

A = 73,000(1.07)⁹

A = 73,000(1.8385)

A = 134,208.52

Deposit value after 9 years would be $ 134,208.52 in Second City Bank.

Therefore, Difference in Account = $ 134,208.52 - $ 118,990

= $ 15,218.51

4.

Deposit (P) = $ 900

Interest Rate (R) = 0.0525

Calculation of Amount (A) after 6 years if interest compounded annually.

A = P(1+R)^T

A = 900(1.0525)⁶

A = 900(1.35935)

A = 1,223.42

Calculation of Amount (A) after 6 years if interest compounded annually.

A = P(1+R)^T

A = 900(1.0525)⁷

A = 900(1.43072)

A = 1,287.65

He will withdraw extra money amounting $ 64.23 ( $ 1.287.65 - $ 1,223.42) if he wait for one more years i.e end of 7th year.