Respuesta :
It will take 3.23 years for the smaller investment to catch up to the larger one with $5000 investment earning 7.2% annual interest, and an $8000 investment earning 5.4%, both compounded annually.
Give a brief account on compound interest.
In other terms, compound interest is interest on principal + interest and refers to the addition of interest to the principal amount of a loan or deposit. Reinvesting interest, or adding it to the lent capital rather than paying it out or requiring payment from the borrower, results in interest being earned on the principal amount plus previously accumulated interest in the next period. In economics and finance, compound interest is common.
In contrast to simple interest, which doesn't compound because past interest isn't added to the principle for the current period, there is compounding with compound interest. The simple annual interest rate is calculated by dividing the period interest by the number of periods in a year.
To solve the question :
Use the compound interest formula:
A = P(1+i)^n
A = amount
P = principal
i = interest per compounding period
n = number of compounding periods
The totals would be equal if the smaller investment eventually catches up to the larger one. As a result, when we combine the two, we get an equation in which n, or the number of periods, is the only unknown.
T = 5000(1.072)^n=8000(1.054)^n
Solve for n:
(1.072/1.054)^n = 8000/5000
take logs and apply laws of logarithm,
n × log(1.072/1.054) = log(8000/5000)
n = log(8000/5000)/log(1.072/1.054)
I get approximately n = 28.
Substituting the value of n in the equation :
T = 5000(1.072)^n=8000(1.054)^n
T = 2.61 = 8.43
T = 3.23
Therefore, it will take 3.23 years for the smaller investment to catch up to the larger one.
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