Question

In: Finance

Provide a story problem that can be solved using one or more of the TVM calculations.

Expert Solution

Time Value of Money (TVM) is an important concept in financial management. It can be used to compare investment alternatives and to solve problems involving loans, mortgages, leases, savings, and annuities.

some formulaes relating to Time Value of Money (TVM)

Lump Sum Formulas
To Solve for	Formula
Future Value	FV=PV(1+i)N
Present Value	PV=FV/(1+i)N
Number of Periods	N=ln(FV/PV)/ln(1+i)

Following are the problems providing you to understand deeply about calculations of Time Value of Money (TVM).

PROBLEM 1:-

If you wish to accumulate $197,000 in 5 years, how much must you deposit today in an account that pays a quoted annual interest rate of 13% with semi-annual compounding of interest?

Answer 1:-

n = 10 (5 years times 2 comp. periods per year) i = 6.5 (13% annually divided by 2 comp. period per year) FV = 197000 solve for PV (answer = $104,947.03)

PROBLEM 2:-

If you deposit $10 in an account that pays 5% interest, compounded annually, how much will you have at the end of 10 years ? 50 years? 100 years ?

Answer 2:-

10 years: FV = $ 10 ( 1+0.05)¹⁰ = $ 10 (1.6289) = $ 16.529

50 years: FV = $ 10 ( 1+0.05)5⁰ = $ 10 (11.4674) = $ 114.67

100 years: FV = $ 10 ( 1+0.05)¹⁰⁰ = $ 10 (131.50) = $ 1315.01

PROBLEM 3:-

How much interest on interest is earned in an account by the end of 5 years if $100,000 is deposited and interest is 4% per year, compounded continuously?

Answer 3:-

Note : Interest on interest is the difference between the future value calculated using compounded interest and the future value calculated using simple interest, because simple interest includes only interest on the principle amount, not the interest on interest.

Continuously compounded:-

FV = $1,00,000 e0.04(5) = $100,000 (1.2214) = $122,140.28

Simple interest:-

FV = $100,000 + {$100,000(0.04)(5)} = $ 100,000+20,000 = $120,000

Interest on interest = $122,140.28 = $ 120,000 = $ 2,140.28

jeff jeffy answered 2 years ago

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