Question

1. You deposit $20,000 today. If it grows to $60,000 in 10 years, what rate of interest must have your earned?

2. Today is T=0. If you make five annual deposits into a bank account that pays interest at the rate of 6%, how large must the deposits be if the account is worth $75,000 at the end of the fifth year (T=5) and the first deposit is made today?
3. You will start college on your 18^th birthday. Your parents need $100,000 on that day. How much should they deposit into a bank account at the moment of your birth if the bank pays interest at the rate of 9%?

Answer 1

Part-1

Given:

Present Value(PV)= $20,000

Future Value(FV)= $60000

Time(t)=10 years

We know that,

[where, FV= Future Value

PV= Present Value

R= rate of Interest

t= Time Period]

Thus,

(using Calculator, )

R= 0.11613

Therefore, Rate of interest earned on the deposit =11.613%

PART-2

Calculation of Annual Deposit to be made for 5 years starting at Year 0

Let the annual Deposits to be made be $

we know that,

[R= rate of interest, T= time period]

(from Annuity Table, PVAF(6%, 4 years)=3.465 )

Annual Deposit to be made each year = $16797.312

PART 3

Given:

Future Value(FV)= $100,000

Time(t)=18 years

Rate of Interest (R)=9%

For Calculating PV ie. amount to be invested at year 0,

PV= $21,200

Therefore, Amount to be deposited at Birth = $21,200