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Your generous grandmother has just announced that she’s opened a savings account for you with a deposit of $10,000. Moreover, she intends to make you 9 more similar gifts, at the end of this year, next year, etc. If the savings account pays 8% interest, how much will you have
accumulated at the end of 10 years (one year after the last gift)?

Sagot :

Tundexi

Answer:

$156,454.87

Explanation:

Future Value of an annuity due: FV = Pmt x ((1+r)n -1))/r) x (1+r)

When Payment per period (PMT) = $10,000, Discount Rate per period= 8%,Number of periods (n) = 10

Future Value = $10,000 * ((1+0.08)^10 -1))/0.08) * 1.08

Future Value = $10,000 * [(1.08)^10 - 1 ]/ 0.08 * 1.08

Future Value = $10,000 * 2.15892499727-1/0.08 * 1.08

Future Value = $10,000 * 1.15892499727/0.08 * 1.08

Future Value = $10,000 * 14.486562465875 * 1.08

Future Value = 156454.87463145

Future Value = $156,454.87

The worth of a collection of regular payments at a future date, assuming a given discount rate, or rate of return (ROR) is called the future value of an annuity.  (FAPThe present value (PV) of an annuity is the amount of money required to fund a series of future annuity payments (FAP) today.

COMPUTATION OF FUTURE VALUE OF ANNUITY DUE:

[tex]\text{Future Value of an annuity due (FV)} =[ \frac{\text{Pmt} \text{ x } ((1+r)^{n}}{r} -1] \text{ x } (1+r)[/tex]

[tex]\text{Where,}\\\text{Payment per period (PMT)} = 10,000, \\\text{Discount Rate per period(r)} = 0.08,\\\text{Number of periods (n)} = 10[/tex]

[tex]\text{(FV)} =[ \frac{\ 10,000 \text{ x } ((1+0.08)^{10}}{0.08} -1] \text{ x } (1+0.08)[/tex]

[tex]\text{(FV)} =[ \frac{\ 10,000 \text{ x } ((1.08)^{10}}{0.08} -1] \text{ x } (1.08)[/tex]

[tex]\text{(FV)} =[ \frac{\ 10,000 \text{ x } 2.1589}{0.08} -1] \text{ x } (1.08)[/tex]

[tex]\text{(FV)} =[ \frac{\ 10,000 \text{ x } 1.15892499727}{0.08} ] \text{ x } (1.08)[/tex]

[tex]\text{(FV)} =[ 10,000 \text{ x } 14.486562465875} ] \text{ x } (1.08)[/tex]

[tex]\text{(FV)} = 156454.87463145[/tex]

[tex]\text{Future Value} = 156,454.87[/tex]

Therefore, the accumulated amount at the end of 10 years is $156,454.87.

For more information regarding the future value (FV), refer to the link:

https://brainly.com/question/13369387

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