Nigel invested $15 000 for 4 years at 8.5% simple interest. At the end of the 4 years he reinvested his total funds at 8% interest compounded annually for a further 3 years.Calculate the final amount of Nigel’s investment at the end of the 7 years.
Question
Nigel invested $15 000 for 4 years at 8.5% simple interest. At the end of the 4 years he reinvested his total funds at 8% interest compounded annually for a further 3 years.Calculate the final amount of Nigel’s investment at the end of the 7 years.
Solution
Sure, let's break this down into two parts: the simple interest for the first 4 years, and the compounded interest for the next 3 years.
- Simple Interest Calculation: The formula for simple interest is I = PRT, where P is the principal amount, R is the rate of interest, and T is the time in years.
So, for the first 4 years, the interest Nigel earns is: I = 5,100
Adding this to the principal, the total amount after 4 years is 5,100 = $20,100.
- Compound Interest Calculation: The formula for compound interest is A = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
In this case, the interest is compounded annually, so n = 1. The principal P is the total amount from the first 4 years, which is $20,100. The rate r is 8%, or 0.08, and the time t is 3 years.
So, the total amount A after 3 years is: A = 20,100 * (1.08)^3 = $26,848.83
So, the final amount of Nigel’s investment at the end of the 7 years is approximately $26,848.83.
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